EMERGENCE OF THE LAWS OF NATURE IN THE DEVELOPING ENTANGLED UNIVERSE
Evgeny A. Novikov
University of California - San Diego, BioCircuits Institute, La Jolla, CA 92093 -0328; E-mail: enovikov@ucsd.edu
Abstract
Evolution of our universe with continuous production of matter by the vacuum, is described. The analysis is based on the quantum modification of the general relativity (Qmoger), supported by the cosmic data without fitting. Various types of matter are selected by the vacuum in accordance with stability of the developing universe. All laws of nature seems to be emergent and approximate, including the conservation of energy. The (3+1)-dimensional space-time and gravity were selected first. Than came quantum condensate of entangled gravitons (dark matter). Photons and other ordinary matter were selected much later during formation of galaxies, when the background condensate becomes gravitationally unstable. The effect of radiation on the global dynamics is described in terms of conservation of the enthalpy density. Mass of neutrino, as the first massive fermionic particle created from the background condensate, is estimated, in accord with experimental bound. The electric dipole moment of neutrino is also estimated. The oscillations of neutrinos are explained in terms of interaction with background condensate. The phenomena of quantum entanglement of ordinary matter was, apparently, inherited from the background condensate. The phenomena of subjective experiences are also explained in terms of interaction of the action potentials of neurons with the background dipolar condensate, which opens a new window into the dark sector of matter. The Qmoger theory goes beyond the Standard Model and the Quantum Field Theory and can be combined with their achievements.
Key words: quantum modification of general relativity, emergence of the laws of nature, isenthalpic universe, quantum condensate of gravitons, oscillating neutrinos, subjective experiences and dark sector of matter.
PDF file at viXra:1712.0456
Published in American Research Journal of Physics, v. 4(1), 1-9 (2018)
1 Introduction
The level of a civilization, to a great extend, is determined by its cosmology. If we, the people, want to survive and prosper, we need to adapt a right cosmology. The fundamental question of physics, including cosmology, is where the laws of nature came from? In this paper we will try to answer this question. Our analysis is based on the quantum modification of general relativity (Qmoger), which is supported by cosmic observations without fitting (including the acceleration of the universe, see below). At the same time, we will advance the theory and get new results.
The Qmoger equations differ from the Einstein equations by two additional terms, which are responsible for production and absorption of matter (see section 3). This is in contrast with the conventional cosmology, which assumes that all matter of the universe was produced 13.7 billion years ago in a singular Big Bang (BB) [1]. The BB hypothesis inspired many important observations, including the resent detection of cosmic gravitational signals. But the BB theory becomes more and more cumbersome in its attempts to overcome contradictions with cosmic data [1-5]. This is a sure sign of a flawed theory. Particularly disturbing are, of course, the singularity of mysterious BB, the physically unexplainable critical density of the universe, the dark energy (ridiculously small cosmological constant with unclear physical sense) and the miraculous inflation (a rescue mission, which does not sit well with BB). The situation with BB theory reminds analogous situation with the geocentric model of Ptolemy. Old habits die hard and a resistance to the new cosmology is expected. But, in my humble opinion, it is time to move on.
2 Space-time and gravity
It seems natural to connect the creation of the universe with some kind of instability of the vacuum. That instability is inducing a release of something, which we, the people, now call matter/energy. It also seems natural that a part of the vacuum becomes metrical to hold the embryonic universe and feed it, not unlike an ovary of a fruit.
Without a prior length scale, the universe presumably adapted the scale -similarity and logarithmic modulations, which is typical for the turbulent flows [6]. So, the appropriate variable for the global evolution of the universe is η(t)=ln[a(t)/a₀], where a(t) is the size of the universe (scale factor) as a function of time and subscript 0 indicates the present epoch (t=0). Corresponding second order differential equation for the continuous evolution can be conveniently written in the form:
η=-ξ, #1
where dots indicate differentiations with respect to time and ξ has dimension of inverse time squire: [ξ]=T⁻². For a limited growth, the simplest assumption about ξ is that it is a positive constant. The general solution of (1) has the Gaussian form:
a(t)=a₀exp[H₀t-(1/2)ξt²], #2
where H₀=η(0) is the Hubble constant. With H₀>0, this solution describes continuous growth from a(-∞)=0 to maximum a_{m}=a₀exp[H₀²/(2ξ)] at t_{m}=H₀/ξ. For t>t_{m}, a(t) continuously decreases to a(-∞)=0. The main parameter of this model is ξ, because H₀ can be eliminated by shifting time. It seems natural to connect ξ with gravity, which restrains the growth. In Ref. 7 it was shown, that universe with spatial dimension 1 and 2 collapses to singularity in a finite time. "Only starting with the spatial dimension 3, universe get an opportunity to survive" [7]. In the (3+1)-dimensional space-time, the gravitational constant G has dimension [G]=M⁻¹L³T⁻². Assuming that ξ∼G, we get [ξ/G]=ML⁻³, which is the dimension of the mass density, which we denote ρ₀. So, we can write: ξ=θGρ₀, where θ is nondimensional. If θ is constant, then ρ₀ is also constant and is important physical parameter, which determines the global dynamics of the universe. In the next section we will derive the described above model from the quantum modification of general relativity (Qmoger) and, based on the Qmoger equations, calculate the value θ=4π. It turn out, that such simple model, without any fitting, is in good quantitative agreement with cosmic data, including the acceleration [see below, particularly, Fig.1 and equation (11)] .
At this stage, we can conclude that gravity is the primary force. The vacuum can, potentially, create and absorb matter with various properties. Gravity serves the purpose of formation a finite compact object - the universe. This requirement of the indicated above instability of the vacuum creates a natural selection of matter. Only gravitating matter survives this selection. 3 Quantum modification of general relativity (Qmoger)
Qmoger equations, introduced in Ref. 3 and discussed in more detail in Ref. 4 and 5, have the form:
R_{i}^{k}-(1/2)δ_{i}^{k}R=8πG_{∗}T_{i}^{k}+λ_{N}δ_{i}^{k},T_{i}^{k}=wu_{i}u^{k}-δ_{i}^{k}p,w=ε+p, #3
λ_{N}=λ₀+β((dσ)/(ds))+γσ²,σ=((∂u^{k})/(∂x^{k}))+(1/(2g))((dg)/(ds)),(d/(ds))=u^{k}(∂/(∂x^{k})). #4
Here R_{i}^{k} is the curvature tensor, p, ε=ρc² and w are pressure, energy density and enthalpy density, respectively, ρ is the mass density, G_{∗}=Gc⁻⁴( c- speed of light), u^{k} - components of velocity (summation over repeated indexes is assumed from 0 to 3, x⁰=τ=ct), λ₀ is the cosmological constant (which we will put zero), σ is the covariant divergency, β and γ are nondimensional parameters (with particular choice β=2γ=2/3, see below) and g is the determinant of the metric tensor. With β=γ=0 we recover the classical equations of GR. Let us note that curvature terms in the left hand side of (3) and additional terms dσ/ds and σ² all contain second order (or square of first order) derivatives of metric tensor, which make these terms compatible. The importance of σ also follows from the fact that it is the only dynamic characteristic of media, which enters into the balance of the proper number density of particles n: dn/ds+σn=q, where q is the rate of particle production (or absorption) by the vacuum. So, if n is constant (see the exact analytical solution (10) below) or changing slowly, than the σ-effect is, certainly, very important in quantum cosmology. The σ-terms were introduces [3] with such physical argumentation on base of previous works [7-9]. Later, in the case β=2γ, equations (3, 4) were derived from the variational principle by simply replacing the cosmological constant λ₀ (in the Lagrangian) by λ=λ₀-γσ²[10]. Indeed, the variation of ∫d⁴x(-g)^{1/2}σ² with respect to the metric tensor produces the two σ-terms in (3, 4) [10]. But, the system is not Hamiltonian, the vacuum is feeding the universe, so, the standard approach is not appropriate¹⁾. Parameters (β,γ), generally, depend on the equation of state (see next section). Some exact analytical solutions of equations (3, 4) where obtained in Ref. 3. On the basis of these solutions, it was concluded that the effect of spacetime stretching (σ) explains the accelerated expansion of the universe and for negative σ (collapse) the same effect can prevent formation of singularity. Equations (3, 4) reproduce Newtonian gravitation in the nonrelativistic asymptotic, but gravitational waves can propagate with speed, which is not necessary equal to speed of light [10]. This give us a hint that gravitons may have finite mass (see section 5).
The natural next step was quantitative comparison with cosmological data and choice of parameters β and γ. Let us consider equations for the scale factor a(t) in homogeneous isotropic universe, derived from (3, 4) by standard procedure [Eq. (8,9) in Ref. 3, or Eq. (3, 4) in Ref. 5]:
(2-3β)(a/a)+(1+3β-9γ)((a/a))²+((kc²)/(a²))-λ₀c²=-8πGpc⁻², #5
-β(a/a)+(1+β-3γ)((a/a))²+((kc²)/(a²))-((λ₀c²)/3)=((8π)/3)Gρ. #6
Here the discrete curvature parameter k=0,+1,-1 corresponds to flat, closed and open universe, respectively.
With indicated in Ref. 3 unique choice β=2γ=2/3, these equations take simple form:
(k/(a²))=λ₀-8πG_{∗}p, #7
η=((3kc²)/(2a²))-((λ₀c²)/2)-4πGρ, #8
where η=ln(a/a₀). From (7) with λ₀=0, we see that sign of curvature is opposite to sign of pressure. From observations we know that global curvature is close to zero. So, the dust approximation (p=0 ) is natural for this theory with λ₀=0 and β=2γ=2/3. In the dust approximation with λ₀=0,k=0, two special cases for system (5, 6) have been indicated [3]: 1) for β=2/3 and γ≠1/3 stationary solution exist; 2) for β=2γ the global energy is conserved, except for β=2γ=2/3. The choice β=2γ=2/3 is exceptional and in the dust approximation with λ₀=0,k=0, equation (7) is identity and (8) reduces to:
η=-4πGρ. #9
In order to solve this equation, we need an assumption about ρ. For a continuous creation of matter by the vacuum, the simplest situation is with constant mass density ρ=ρ₀. In Ref. 5 and in the next section some more general situations are considered. With constant mass density, from (9) we have exact analytical Gaussian solution:
a(t)=a₀exp[H₀t-2πGρ₀t²] #10
So, in this case, from Qmoger we got the same solution as in the model (2), but now with fixed constant ξ=4πGρ₀. In the analogous solution, obtained in Ref.10, instead of ε₀ was ρ₀+(λ₀c²)/(8πG), for generality. We use value ρ₀≈2.6⋅10⁻³⁰gcm⁻³, which, according to WMAP [12], includes ordinary and dark matter. We do not include the dark energy, which does not exist in Qmoger (see below). For the characteristic time scale we have (Gρ₀)^{-1/2}= T_{∗}≈76 billion years (by). Corresponding length scale L_{∗}=cT_{∗}≈76 billion light years (bly) is comparable with the current size of the visible universe a₀≈46.5 bly. We use recently measured [13] value H₀=70.0(km/s)/Mpc≈2.27⋅10⁻¹⁸s⁻¹. Remarkably, T_{∗}H₀≈5.27. The temporal scale H₀⁻¹ and the eternal scale T_{∗} are of the same order because currently a(t) is relatively close to its maximum a_{m}≈ 3.24a₀ at time t_{m}=(T_{∗}²H₀)/(4π)≈32.9 by. It was shown [10], that solution (10) is globally stable during expansion (-∞t_{max}.
From (10) we get current acceleration parameter:
((a₀a₀)/((a₀)²))=1-4πGρ₀H₀⁻²≈0.58. #11
So, we do not need the dark energy in order to explain the acceleration. According to (10), with indicated above values of H₀ and ρ₀, the maximum of velocity a≈0.093c will be at t≈11.7by. Note, that measurements of H₀, generally, give different results for different galaxies and the background radiation is anisotropic. According to Qmoger, it seems natural. Formation of galaxies and corresponding radiation are results of gravitational instability of the background quantum condensate (see section 5). So, galaxies do not have to be synchronized during expansion of the universe. The same is true for radiation. The BB theory has difficulties to explain these cosmic observations. The BB theory also has difficulty to explain some old structures in the universe, for example, recently discovered an 800-million-solar-mass black hole in a significantly neutral universe at redshift z=a₀/a-1= 7.5 [14].
Solution (10) does not have any fitting parameters and is in good quantitative agreement with cosmic data [10, 15, 4], see also Fig. 1 below. This solution eliminates not only singularity of Big Bang, but also other major controversies - critical density of the universe (which is difficult to explain physically), dark energy (ridiculously small cosmological constant) and inflation (which does not sit well with Big Bang). Remarkably, solution (10) does not depend on the speed of light c. That is because, according to Qmoger, there was not much light in the beginning. Photons and other "ordinary" matter were selected and actively produced much later during formation of galaxies (see below). Even at the later stages, the contribution of light into the total energy of the universe is small.
4 Isenthalpic universe
To consider the effect of radiation on the global dynamics, we rewrite equations (5, 6) in the form:
η=-4πGwc⁻²+kc²a⁻², #12 Note, that equation (12) does not have parameters λ₀,β,γ and is the same for the classical GR. In order to solve the system (12, 13), we need some form of the equation of state. The popular approximation p=ϰε (with constant ϰ) was considered in Ref. 5. Equation (12) suggests a different possibility. A novel approximation is to assume that the enthalpy density is constant: w=ρc²+p=w₀. This will allow the pressure to grow and a part of the energy to radiate, for example, during formation and interaction of stars. With that approximation, we can solve equation (12) for any curvature parameter k and get pressure from (13). Particularly, for k=0, equation (12) gives:
η=H₀-4πGw₀c⁻²t, a(t)=a₀exp[H₀t-2πGw₀c⁻²t²]. #14
This solution differs from (10) by substitution w₀c⁻² instead of ρ₀. The difference is small, because the averaged pressure in the universe is small in comparison with the energy density. For solution of Einstein equation (β=γ=0) with k=0, from (13, 14) we get:
8πGε=3(H₀-4πGw₀c⁻²t)²-λ₀c⁴, p=w₀-ε #15
From (15), we see that ε→∞ and p→-∞ with t→±∞, which is unphysical.
In Qmoger we can avoid such contradiction with reality. During formation and interaction of stars, parameters β and γ are, generally, no longer constant. For isenthalpic processes (w=w₀) we can assume (β,γ) to be functions of p/w₀. A simple model for deviation from used above values β=2/3, γ=1/3, has the form:
β=(2/3)[1-b((p/(w₀)))²], γ=(1/3)[1+χ((p/(w₀)))²], #16
where b and χ are positive constants. Substitution of (16) into (13), with λ₀=0 and k=0, gives nontrivial solution:
(p/w)=((8πGw₀)/(8πGw₀b+χ(H₀c-4πGw₀c⁻¹t)²)), ε=w₀-p. #17
According to (17), the averaged pressure increases from 0 at t=-∞, riches maximum p_{m}=w₀/b at t_{w}=H₀c²/(4πGw₀) and decreases to 0 at t=∞. Averaged energy density starts with ε=w₀ at t=-∞, decreases to minimum w₀(1-1/b) at τ_{w} and then return to the original value w₀. Such behavior of averaged pressure and energy seems physically reasonable. Part of the energy, radiated during formation and interaction of stars, absorbs in contraction. Positivity of energy (ε>0) gives restriction on parameter b>1.
Choice of isenthalpic process is dictated by the form of Einstein and Qmoger equations and leads to simple Gaussian solution (14). We can speculate that such processes are wide spread in Nature and wait to be discovered.
Let us stress, that solution of Einstein equations (with β=γ=0) and solution of Qmoger equations give the same result (14), corresponding to cosmic data with w≈ε₀ (see Figure 1). But asymptotics ε→∞ and p→-∞ with t→±∞ in solution of Einstein equation (15) looks unphysical.
Formulas (16) can be used also for local calculation of galaxies formation with Qmoger equations. More details can be obtained by inclusion electromagnetic terms into Qmoger equations. Isenthalpic processes of dipolar gravitons (see below) can produce radiation and magnetic field not only in stars (such as our sun), but also in a planet core. Excessive radiation of Jupiter and Saturn [16] could be connected with this phenomena. More details can be obtained by introducing into the basic equations (3, 4) additional fields (Qmoger+), particularly, the electromagnetic field.
5 Entangled universe: quantum condensate of gravitons - dark matter, critical size of condensate and quantum gravitational waves
In seems natural, that the quantum interaction was selected in order to keep the early universe as a compact quantum condensate, which will resist the gravitational instability. The quantum uncertainty condition with indicated above time scale T_{∗} corresponds to energy E₀=ħ/T_{∗}≈ 4. 17⋅10⁻⁴⁶erg≈2. 61⋅10⁻³⁴eV, where ħ is the Planck constant. That is the unique energy, determined by parameters G, ρ₀ and ħ. Corresponding mass of a particle is m₀=ħ/(c²T_{∗})≈4.6⋅10⁻⁶⁷gram. This particle we call graviton, because only gravity field was used in the theory. In this paper we will not compare such definition of graviton with many definitions and use of gravitons in the literature [17]. Let us only stress, that Qmoger theory is not Hamiltonian ( see section 3). Gravitons in this theory are not virtual, but real particles with small, but finite mass m₀ [compare with electron mass m_{e}∼9⋅10⁻²⁹gram] and, possibly, with some electromagnetic properties (see section 7).
Taking into account, that the dark matter dominate the mass content of the universe, the concentration of particles n and characteristic scale l (averaged distance between particles) can be estimated as:
n=ρ₀/m₀≈5⋅10³⁶, l=n^{-1/3}≈2.7⋅10⁻¹³cm. #18
Such particles will form the quantum condensate even for high temperature [4, 5]. Indeed, the thermal de Brogle wavelength for the temperature of the universe T≈2.72K is many orders bigger than l: ħc/(k_{B}Tl)≈3⋅10¹¹ (k_{B} - Boltzmann constant). This estimate is for massless particles. For nonrelativistic gravitons with indicated above mass m₀, the corresponding factor is even bigger: ħ(m₀k_{B}T)^{-1/2}l⁻¹≈7⋅10¹³. So, gravitons are entangled in the quantum condensate.
To estimate time t_{g}, when such gravitons can be created, we use condition a(t_{g})=l. From (10) we have:
t/T_{∗}=ζ±[ζ²-η/(2π))]^{1/2}, ζ=(T_{∗}H₀)/(4π)≈0.43. #19
Here minus correspond to the past. For η_{g}=ln(l/a₀)≈-91, from (19) we got t_{g}≈ -258 by. For a while, the growing universe, supported by the quantum interaction, will resist the gravitational instability. The critical size of the quantum gravitating condensate l_{cr}, for arbitrary ρ, is uniquely determined by parameters (G,ρ,ħ). Namely:
l_{cr}=ħ^{1/5}G^{-1/10}ρ^{-3/10}. #20
As expected, l_{cr} is increasing with increase of ħ and decreasing with increase of G and ρ. Particularly, at ρ=ρ₀, we get l_{cr,0}=ħ^{1/5}G^{-1/10}ρ₀^{-3/10}≈1. 498⋅10⁶cm≈15km. Corresponding time t_{cr}, when embryonic galaxies start to form, is determined by (19) with η_{cr}=ln(l_{cr,0}/a₀)≈-51. 7. The result is t_{cr}≈-187. 5by.So, it took 70.5 by of graviton production to initiate formation of galaxies. Corresponding critical mass m_{cr}=ρ₀l_{cr}³=ħ^{3/5}G^{=3/10}ρ₀^{1/10}≈ 8. 74⋅10⁻¹²g. Important nondimensional parameter of the theory is the critical number of gravitons N_{cr}=m_{cr}/m₀=ħ^{-2/5}G^{-4/5}ρ₀^{-2/5}c²=(c/u_{ħ,0})²≈ 1. 9⋅10⁵⁵. Here u_{ħ,0}=(ħG²ρ₀)^{1/5}≈ 6. 51⋅10⁻¹⁵cms⁻¹. This is a particular case of speed u_{ħ}=(ħG²ρ)^{1/5} of quantum gravitational waves in the condensate, which is uniquely determined by parameters (G,ρ,ħ). The obtained small value of u_{ħ,0} corresponds to small averaged mass density ρ₀. During formation of galaxies and interactions of stars, local ρ, potentially, can approach the Planck density ρ_{P}=c⁵/(ħG²) and local u_{ħ} can be comparable with c. Formula (20) can be applied to the blobs of dark matter in the halo of galaxies.
6 Creation of neutrinos from the background gravitons
Due to the collapsing mechanism, described in Ref. 7, some hot spots were developing during formation of galaxies. So, there is a necessity to get rid of an excessive energy. Apparently, photons were selected out of this necessity.
The next step in getting rid of excessive energy is selection of fermionic massive particles, which obey the Pauli exclusive principle and will run away from hot spots. Apparently, creation of new particles does not depend directly from gravity. We see it on example of photons, which are characterized only by parameters c and ħ. From these two parameters, which have dimensions [c]=LT⁻¹ and [ħ]=ML²T⁻¹, we can not construct a mass. That is why, the Standard Model can not predict absolute value of mass for observable particles. If G is included, than parameters (c,ħ,G) give uniquely the Planck mass m_{P}=(ħc/G)^{1/2}≈2.176⋅10⁻⁵gram, which is many orders heavier than observable particles (for example, mass of electron m_{e}≈9.11⋅10⁻²⁸gram).
In Qmoger theory, from parameters (c,ħ,ρ₀) we get unique mass:
m_{∗}=ρ₀^{1/4}(ħ/c)^{3/4}≈ 3. 13⋅10⁻³⁶gram≈1.76⋅10⁻³eV/c². #21
From the same parameters, we get unique length scale:
l_{∗}=(ħ/(cm_{∗}))=(((m_{∗})/(ρ₀)))^{1/3}=((ħ/(cρ₀)))^{1/4}≈10⁻²cm. #22
The obtained scale l_{∗} corresponds to the Compton wavelength of a particle with mass of background matter occupying volume of size l_{∗}. This indicates a mechanism of formation new particles from the background matter. We associate the obtained mass (21) with the first and the lightest massive fermionic particle created from the background condensate. The best candidate for that role from the observable particles is neutrino. Indeed, m_{∗} satisfies the experimental upper limit for neutrinos ∼4⋅10⁻²eV/c² [17]. Taking into account that m_{∗} is obtained from dimensional analysis, a moderate numerical factor is expected. The time scale:
t_{∗}=((ħ/(c⁵ρ₀)))^{1/4}≈3.3⋅10⁻¹³s #23
can be associated with formation and acceleration (c/t_{∗}≈8.46⋅10²²cms⁻²) of neutrino, as well as to the neutrino oscillations (transformation between three flavours) [18]. The physics of these oscillations can be related to interaction of neutrino with the background condensate of ultralight gravitons. The averaged number of gravitons interacting with such neutrino can be estimated by N_{∗}=m_{∗}/m₀=N_{cr}^{5/8}≈10³⁰. Below we will estimate the electric dipole moments (EDM) of both gravitons and neutrinos, which can be a significant factor of interactions. During its flight, neutrino can create some disturbances in the background condensate and temporary carry along coherent groups of gravitons, perhaps, in a form of vortex ring. This will influence the effective mass and the flavor of neutrino [17]. This an example of interface between dark and ordinary matter (Idom), introduced in context of explanation of the phenomena of subjective experiences (qualia) [19] (see also section 9). Note, that in frames of the Standard Model, the stability of all three neutrinos (v_{e},ν_{μ},ν_{τ}) was a long-time puzzle. In Qmoger, stability of the first-generation particles (neutrinos), produced by the background condensate, is natural.
7 Electric dipole moment of graviton and neutrino.
The baryonic asymmetry of the universe ( prevalence of matter over antimatter ) can be explained if gravitons have nonzero electric dipole moment (EDM). Indeed, EDM of primary particles can break the reflection symmetry and give advantage to matter over antimatter. It will also help to explain synthesis of some particles from the dipolar quantum condensate. Additionally, EDM of gravitons helps to explain qualia [19] and brightens the dark sector of matter (see below).
Technically, it is more simple to estimate EDM of neutrino, because, as explained above, properties of neutrino do not affected directly by G. From parameters (c,ħ,ρ₀) we get unique expression for EDM of neutrino or similar first-generation particle, produced by the the background condensate:
d_{∗}=(((ħ³c)/(ρ₀)))^{1/2}≈5.8⋅10⁼¹¹g^{1/2}cm^{5/2}s⁻¹≈ 0.12ecm. #24
For gravitons we have additional parameter G. The general expression for EDM of graviton, from dimensional argument, can be written in the form: d₀=d_{∗}F(m₀/m_{∗}) with arbitrary function F. If we assume that EDM of graviton is proportional to its mass, than d₀∼1.2⋅10⁻²⁹ecm. In Ref. 4, 5 it was suggested that d₀∼m₀^{1/2}l_{P}^{3/2}c∼2⋅10⁻⁷²gram^{1/2}cm^{1/2}s⁻¹, where l_{P} =(ħG/c³)^{1/2}≈1.6⋅10⁻³⁷cm is the Planck length. In any case, d₀ is very small and conventional telescopes can not see gravitons (dark matter). It also very difficult to detect gravitons in the supercollider or in any high energy machine. But, in section 9 we consider a novel approach to study gravitons.
8 Vacumo
The solution (10) of the partial differential equations (3, 4) is valid under condition a(t)≥l_{P}, which corresponds to sufficiently smooth space-time. In frames of Qmoger, the time t₁ of the beginning of the universe is naturally determined by equation a(t₁)=l_{P}. From (10), we get t₁≈-327by [20, 4, 5]. So, there was t_{g}-t₁ ≈68by of feeding the infant universe before it was able to produce gravitons. The time t₁ corresponds to the mass of the universe M₁=ρ₀l_{P}³≈10⁻¹²⁸gram (recall, that the mass of graviton m₀≈4.6⋅10⁻⁶⁷gram). That results suggest existence of particles or quasiparticles with energy smaller than E₀≈2. 61⋅10⁻³⁴eV. If such particle has the rest mass, it is smaller than m₀. Any such particle we call vacumo. Apparently, the universe is feeding by vacumos, which than transform into gravitons. Vacumos also can play a role of mediators between gravitons and ordinary matter, particularly, in formation of neutrinos (see above).
In Ref. 10 is was argued, that dark matter particle (which we now call gravitons, see above) consists of a pair of massive photons. They do not have to be ordinary photons, but photon-like particles. That is consistent with EDM of gravitons (see above).
9 Qualia
In our subjective experiences (qualia) we can actually see and feel the collective effects of the background gravitons [19]. The acting potentials of neurons [21], apparently, create gaps and coherent patterns in the condensate of gravitons. Remarkably, these interfaces between dark and ordinary matter (Idom) in cases of neutrino and qualia are similar. Note, that length scale (22) is of the same order as the size of the neuron cluster, which can produce sufficiently rich qualia. The necessary for qualia huge number of degrees of freedom is supplied by the indicated in section 6 number of gravitons N_{∗}≈10³⁰. It will not be surprising if oscillating neutrinos, which interact with gravitons (see above), play a role in qualia along with the acting potentials of neurons. At the same time, artificial sources of neutrino in a laboratory setting, potentially, can be used for healing and stimulation of the brain. By manipulating with acting potentials and quantifying qualia responses, we can open a new window into the dark sector of matter.
10 Conclusions>br> This paper presents a beginning of a new type of theory, in which the laws of nature are evolving along with the evolution of the universe. The laws of nature seems to be approximate in connection with the feeding of the universe by the vacuum and because of the indicated above instabilities (see also below). Particularly, the conservation of energy emerged when there was already enough energy, so, that additional feeding has small effect on the local balance of energy. The universe is an open (non-Hamiltonian) system. The evolution of the universe was started with selection of the (3+1)-dimensional space-time and gravity, as a stable situation for the beginning. Then came the quantum condensate of entangled gravitons for an additional stabilization. When this condensate becomes gravitationally unstable, the production of ordinary matter (photons, neutrino and more heavy particles) was selected as a relieve from excessive energy in hot spots. The phenomena of quantum entanglement of ordinary matter was, apparently, inherited from the background condensate. From the human point of view, the highest present achievement of the developing universe, of course, is qualia, which was produced by the interface between gravitons and ordinary matter.
In future, we can combine the Standard model and the Quantum Field Theory with Qmoger. This will definitely open new directions of research in physics and biophysics.
¹⁾Note, that Newton and Einstein did not use the Lagrangian, the Hamiltonian and the variational principle. Unfortunately, these days the physical and common sense are often replaced by the variational principle. We can blame textbooks, which are convenient to base on the variational principle. In my opinion, it can lead theoretical physics astray. The non-Hamiltonian Qmoger theory with its seeping gravitons, apart from correcting cosmology, could also help to correct some of deficiencies in the Quantum Field Theory, particularly, the inequivalent representations [11]. Indeed, the active background can eliminate unstable representations of reality.
References
[1] https://en.wikipedia.org/wiki/Big_Bang
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[18] https://en.wikipedia.org/wiki/Neutrino
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[21] https://en.wikipedia.org/wiki/Action_potential.
[Figure]
Fig.1. Comparison of exact analytical solution (2) with results of two observational projects and with some parametric models (details in Ref. 10, 14). Here z=a₀/a-1 is the redshift, m-M is the distance module as function of z, m and M are apparent and absolute magnitudes of the source correspondingly. The observations are model-independent.
PDF file in viXra:1712.0456

EMERGENCE OF THE LAWS OF NATURE IN THE DEVELOPING UNIVERSE
Evgeny A. Novikov
University of California - San Diego, BioCircuits Institute, La Jolla, CA 92093 -0328; E-mail: enovikov@ucsd.edu
Abstract
Evolution of our universe with continuous production of matter by the vacuum, is described. The analysis is based on the quantum modification of the general relativity (Qmoger), supported by the cosmic data without fitting. Various types of matter are selected by the vacuum in accordance with stability of the developing universe. All laws of nature are emergent and approximate, including the conservation of energy. The (3+1)-dimensional space-time and gravity were selected first. Than came quantum condensate of gravitons (dark matter). Photons and other ordinary matter were selected much later during formation of galaxies, when the background condensate becomes gravitationally unstable. The effect of radiation on the global dynamics is described in terms of conservation of the enthalpy density. Mass and electric dipole moment of neutrino (as the first massive fermionic particle) are estimated. The oscillations of neutrinos are explained in terms of interaction with background condensate. The phenomena of subjective experiences are also explained in terms of interaction of the action potentials of neurons with the background dipolar condensate.
1 Introduction
The level of a civilization is, basically, determined by its cosmology. If we, the people, want to survive and prosper, we need to adapt a right cosmology. The fundamental question of physics, including cosmology, is where the laws of nature came from? In this paper we will try to answer this question. Our analysis is based on the quantum modification of general relativity (Qmoger), which is supported by cosmic observations without fitting (including the acceleration of the universe, see below). At the same time, we will advance the theory and get some new results.
The Qmoger equations differ from the Einstein equations by two additional terms, which are responsible for production and absorption of matter (see section 3). This is in contrast with the conventional cosmology, which assumes that all matter of the universe was produced 13.7 billion years ago in a singular Big Bang (BB) [1]. The BB hypothesis inspired many useful observations. But the BB theory becomes very cumbersome and is in agony under contradictions with cosmic data [1-5]. Particularly disturbing are, of course, the singularity of BB, the physically unexplainable critical density of the universe, the dark energy (ridiculously small cosmological constant with unclear physical sense) and inflation (which does not sit well with BB). The situation with BB theory reminds analogous situation with the geocentric model of Ptolemy. It is time to move on.
2 Space-time and gravity
It seems natural to connect the creation of the universe with some kind of instability of the vacuum. That instability is inducing a release of something, which we, the people, now call matter/energy. It also seems natural that a part of the vacuum becomes metrical to hold the embryonic universe and feed it, not unlike an ovary of a fruit.
Without a prior length scale, the universe presumably adapted the scale -similarity and logarithmic modulations, which is typical for the turbulent flows [6]. So, the appropriate variable for the global evolution of the universe is η(t)=ln[a(t)/a₀], where a(t) is the size of the universe (scale factor) as a function of time and subscript 0 indicates the present epoch (t=0). Corresponding second order differential equation for the continuous evolution can be conveniently written in the form:
η=-ξ, #1
where dots indicate differentiations with respect to time and ξ has dimension of inverse time squire: [ξ]=T⁻². For a limited growth, the simplest assumption about ξ is that it is a positive constant. The general solution of (1) has the Gaussian form:
a(t)=a₀exp[H₀t-(1/2)ξt²], #2
where H₀=η(0) is the Hubble constant. With H₀>0, this solution describes continuous growth from a(-∞)=0 to maximum a_{m}=a₀exp[H₀²/(2ξ)] at t_{m}=H₀/ξ. For t>t_{m}, a(t) continuously decreases to a(-∞)=0. The main parameter of this model is ξ, because H₀ can be eliminated by shifting time. It seems natural to connect ξ with gravity, which restrains the growth. In Ref. 7 it was shown, that universe with spatial dimension 1 and 2 collapses to singularity in a finite time. " Only starting with the spatial dimension 3, universe get an opportunity to survive" [7]. In the (3+1)-dimensional space-time, the gravitational constant G has dimension [G]=M⁻¹L³T⁻². Assuming that ξ∼G, we get [ξ/G]=ML⁻³, which is the dimension of the mass density, which we denote ρ₀. So, we can write: ξ=θGρ₀, where θ is nondimensional. If θ is constant, then ρ₀ is also constant and is important physical parameter, which determines the global dynamics of the universe. In the next section we will derive the described above model from the quantum modification of general relativity (Qmoger) and, based on the Qmoger equations, calculate the value θ=4π. It turn out, that such simple model, without any fitting, is in good quantitative agreement with cosmic data, including the acceleration [see below, particularly, Fig.1 and equation (11)] .
At this stage, we can conclude that gravity is the primary force. The vacuum can, potentially, create and absorb matter with various properties. Gravity serves the purpose of formation a finite compact object - the universe. This requirement of the indicated above instability of the vacuum creates a natural selection of matter. Only gravitating matter survives this selection.
3 Quantum modification of general relativity (Qmoger)
Qmoger equations, introduced in Ref. 3 and discussed in more detail in Ref. 4 and 5, have the form:
R_{i}^{k}-(1/2)δ_{i}^{k}R=8πG_{∗}T_{i}^{k}+λ_{N}δ_{i}^{k},T_{i}^{k}=wu_{i}u^{k}-δ_{i}^{k}p,w=ε+p, #3
λ_{N}=λ₀+β((dσ)/(ds))+γσ²,σ=((∂u^{k})/(∂x^{k}))+(1/(2g))((dg)/(ds)),(d/(ds))=u^{k}(∂/(∂x^{k})). #4
Here R_{i}^{k} is the curvature tensor, p, ε=ρc² and w are pressure, energy density and enthalpy density, respectively, ρ is the mass density, G_{∗}=Gc⁻⁴( c- speed of light), u^{k} - components of velocity (summation over repeated indexes is assumed from 0 to 3, x⁰=τ=ct), λ₀ is the cosmological constant (which we will put zero), σ is the covariant divergency, β and γ are nondimensional parameters (with particular choice β=2γ=2/3, see below) and g is the determinant of the metric tensor. With β=γ=0 we recover the classical equations of GR. Let us note that curvature terms in the left hand side of (3) and additional terms dσ/ds and σ² all contain second order (or square of first order) derivatives of metric tensor, which make these terms compatible. The importance of σ also follows from the fact that it is the only dynamic characteristic of media, which enters into the balance of the proper number density of particles n: dn/ds+σn=q, where q is the rate of particle production (or absorption) by the vacuum. So, if n is constant (see the exact analytical solution (10) below) or changing slowly, than the σ-effect is, certainly, very important in quantum cosmology. The σ-terms were introduces [3] with such physical argumentation on base of previous works [7-9]. Later, in the case β=2γ, equations (3, 4) were derived from the variational principle by simply replacing the cosmological constant λ₀ (in the Lagrangian) by λ=λ₀-γσ²[10]. Indeed, the variation of ∫d⁴x(-g)^{1/2}σ² with respect to the metric tensor produces the two σ-terms in (3, 4) [10]. But, the system is not Hamiltonian, the vacuum is feeding the universe, so, the standard approach is not appropriate¹⁾. Parameters (β,γ), generally, depend on the equation of state (see next section).
Some exact analytical solutions of equations (3, 4) where obtained in Ref. 3. On the basis of these solutions, it was concluded that the effect of spacetime stretching (σ) explains the accelerated expansion of the universe and for negative σ (collapse) the same effect can prevent formation of singularity. Equations (3, 4) reproduce Newtonian gravitation in the nonrelativistic asymptotic, but gravitational waves can propagate with speed, which is not necessary equal to speed of light [10]. This give us a hint that gravitons may have finite mass (see section 5).
The natural next step was quantitative comparison with cosmological data and choice of parameters β and γ. Let us consider equations for the scale factor a(t) in homogeneous isotropic universe, derived from (3, 4) by standard procedure [Eq. (8,9) in Ref. 3, or Eq. (3, 4) in Ref. 5]:
(2-3β)(a/a)+(1+3β-9γ)((a/a))²+((kc²)/(a²))-λ₀c²=-8πGpc⁻², #5
-β(a/a)+(1+β-3γ)((a/a))²+((kc²)/(a²))-((λ₀c²)/3)=((8π)/3)Gρ. #6
Here the discrete curvature parameter k=0,+1,-1 corresponds to flat, closed and open universe, respectively.
With indicated in Ref. 3 unique choice β=2γ=2/3, these equations take simple form:
(k/(a²))=λ₀-8πG_{∗}p, #7
η=((3kc²)/(2a²))-((λ₀c²)/2)-4πGρ, #8
where η=ln(a/a₀). From (7) with λ₀=0, we see that sign of curvature is opposite to sign of pressure. From observations we know that global curvature is close to zero. So, the dust approximation (p=0 ) is natural for this theory with λ₀=0 and β=2γ=2/3. In the dust approximation with λ₀=0,k=0, two special cases for system (5, 6) have been indicated [3]: 1) for β=2/3 and γ≠1/3 stationary solution exist; 2) for β=2γ the global energy is conserved, except for β=2γ=2/3. The choice β=2γ=2/3 is exceptional and in the dust approximation with λ₀=0,k=0, equation (7) is identity and (8) reduces to:
η=-4πGρ. #9
In order to solve this equation, we need an assumption about ρ. For a continuous creation of matter by the vacuum, the simplest situation is with constant mass density ρ=ρ₀. In Ref. 5 and in the next section some more general situations are considered. With constant mass density, from (9) we have exact analytical Gaussian solution:
a(t)=a₀exp[H₀t-2πGρ₀t²] #10
So, in this case, from Qmoger we got the same solution as in the model (2), but now with fixed constant ξ=4πGρ₀. In the analogous solution, obtained in Ref.10, instead of ε₀ was ρ₀+(λ₀c²)/(8πG), for generality.
We use value ρ₀≈2.6⋅10⁻³⁰gcm⁻³, which, according to WMAP [12], includes ordinary and dark matter. We do not include the dark energy, which does not exist in Qmoger (see below). For the characteristic time scale we have (Gρ₀)^{-1/2}= T_{∗}≈76 billion years (by). Corresponding length scale L_{∗}=cT_{∗}≈76 billion light years (bly) is comparable with the current size of the visible universe a₀≈46.5 bly. We use recently measured [13] value H₀=70.0(km/s)/Mpc≈2.27⋅10⁻¹⁸s⁻¹. Remarkably, T_{∗}H₀≈5.27. The temporal scale H₀⁻¹ and the eternal scale T_{∗} are of the same order because currently a(t) is relatively close to its maximum a_{m}≈ 3.24a₀ at time t_{m}=(T_{∗}²H₀)/(4π)≈32.9 by. It was shown [10], that solution (10) is globally stable during expansion (-∞t_{max}.
From (10) we get current acceleration parameter:
((a₀a₀)/((a₀)²))=1-4πGρ₀H₀⁻²≈0.58. #11
So, we do not need the dark energy in order to explain the acceleration. Note, that measurements of H₀, generally, give different results for different galaxies and the background radiation is anisotropic. According to Qmoger, it seems natural. Formation of galaxies and corresponding radiation are results of gravitational instability of the background quantum condensate (see section 5). So, galaxies do not have to be synchronized during expansion of the universe. The same is true for radiation. The BB theory has difficulties to explain these cosmic observations.
Solution (10) does not have any fitting parameters and is in good quantitative agreement with cosmic data [10, 14, 4], see also Fig. 1 below. This solution eliminates not only singularity of Big Bang, but also other major controversies - critical density of the universe (which is difficult to explain physically), dark energy (ridiculously small cosmological constant) and inflation (which does not sit well with Big Bang). Remarkably, solution (10) does not depend on the speed of light c. That is because, according to Qmoger, there was not much light in the beginning. Photons and other "ordinary" matter were selected and actively produced much later during formation of galaxies (see below). Even at the later stages, the contribution of light into the total energy of the universe is small.
4 Isenthalpic universe
To consider the effect of radiation on the global dynamics, we rewrite equations (5, 6) in the form:
η=-4πGwc⁻²+kc²a⁻², #12
8πGp=3(3γ-1)η²+4π(2-3β)Gw-3(1-β)kc⁴a⁻²+λ₀c⁴. #13
Note, that equation (12) does not have parameters λ₀,β,γ and is the same for the classical GR. In order to solve the system (12, 13), we need some form of the equation of state. The popular approximation p=ϰε (with constant ϰ) was considered in Ref. 5. Equation (12) suggests a different possibility. A novel approximation is to assume that the enthalpy density is constant: w=ρc²+p=w₀. This will allow the pressure to grow and a part of the energy to radiate, for example, during formation and interaction of stars. With that approximation, we can solve equation (12) for any curvature parameter k and get pressure from (13). Particularly, for k=0, equation (12) gives:
η=H₀-4πGw₀c⁻²t, a(t)=a₀exp[H₀t-2πGw₀c⁻²t²]. #14
This solution differs from (10) by substitution w₀c⁻² instead of ρ₀. The difference is small, because the averaged pressure in the universe is small in comparison with the energy density. For solution of Einstein equation (β=γ=0) with k=0, from (13, 14) we get:
8πGε=3(H₀-4πGw₀c⁻²t)²-λ₀c⁴, p=w₀-ε #15
From (15), we see that ε→∞ and p→-∞ with t→±∞, which is unphysical.
In Qmoger we can avoid such contradiction with reality. During formation and interaction of stars, parameters β and γ are, generally, no longer constant. For isenthalpic processes (w=w₀) we can assume (β,γ) to be functions of p/w₀. A simple model for deviation from used above values β=2/3, γ=1/3, has the form:
β=(2/3)[1-b((p/(w₀)))²], γ=(1/3)[1+χ((p/(w₀)))²], #16
where b and χ are positive constants. Substitution of (16) into (13), with λ₀=0 and k=0, gives nontrivial solution:
(p/w)=((8πGw₀)/(8πGw₀b+χ(H₀c-4πGw₀c⁻¹t)²)), ε=w₀-p. #17
According to (17), the averaged pressure increases from 0 at t=-∞, riches maximum p_{m}=w₀/b at t_{w}=H₀c²/(4πGw₀) and decreases to 0 at t=∞. Averaged energy density starts with ε=w₀ at t=-∞, decreases to minimum w₀(1-1/b) at τ_{w} and then return to the original value w₀. Such behavior of averaged pressure and energy seems physically reasonable. Part of the energy, radiated during formation and interaction of stars, absorbs in contraction. Positivity of energy (ε>0) gives restriction on parameter b>1.
Choice of isenthalpic process is dictated by the form of Einstein and Qmoger equations and leads to simple Gaussian solution (14). We can speculate that such processes are wide spread in Nature and wait to be discovered.
Let us stress, that solution of Einstein equations (with β=γ=0) and solution of Qmoger equations give the same result (14), corresponding to cosmic data with w≈ε₀ (see Figure 1). But asymptotics ε→∞ and p→-∞ with t→±∞ in solution of Einstein equation (15) looks unphysical.
Formulas (16) can be used also for local calculation of galaxies formation with Qmoger equations. More details can be obtained by inclusion electromagnetic terms into Qmoger equations. Isenthalpic processes of dipolar gravitons (see below) can produce radiation and magnetic field not only in stars (such as our sun), but also in a planet core. Excessive radiation of Jupiter and Saturn [15] could be connected with this phenomena.
5 Quantum interaction, dark matter, critical size of condensate and quantum gravitational waves
In seems natural, that the quantum interaction was selected in order to keep the early universe as a compact quantum condensate, which will resist the gravitational instability. The quantum uncertainty condition with indicated above time scale T_{∗} corresponds to energy E₀=ħ/T_{∗}≈ 4. 17⋅10⁻⁴⁶erg≈2. 61⋅10⁻³⁴eV, where ħ is the Planck constant. That is the unique energy, determined by parameters G, ρ₀ and ħ. Corresponding mass of a particle is m₀=ħ/(c²T_{∗})≈4.6⋅10⁻⁶⁷gram. This particle we call graviton, because only gravity field was used in the theory. In this paper we will not compare such definition of graviton with many definitions and use of gravitons in the literature [16]. Let us only stress, that Qmoger theory is not Hamiltonian ( see section 3). Gravitons in this theory are not virtual, but real particles with small, but finite mass m₀ [compare with electron mass m_{e}∼9⋅10⁻²⁹gram] and, possibly, with some electromagnetic properties (see section 7).
Such ultralight particles will form quantum condensate even for high temperature [4, 5]. Taking into account, that the dark matter dominate the mass content of the universe, the concentration of particles n and characteristic scale l (averaged distance between particles) can be estimated as:
n=ρ₀/m₀≈5⋅10³⁶, l=n^{-1/3}≈2.7⋅10⁻¹³cm. #18
To estimate time t_{g}, when such gravitons can be created, we use condition a(t_{g})=l. From (10) we have:
t/T_{∗}=ζ±[ζ²-η/(2π))]^{1/2}, ζ=(T_{∗}H₀)/(4π)≈0.43. #19
Here minus correspond to the past. For η_{g}=ln(l/a₀)≈-91, from (19) we got t_{g}≈ -258 by. For a while, the growing universe, supported by the quantum interaction, will resist the gravitational instability. The critical size of the quantum gravitating condensate l_{cr}, for arbitrary ρ, is uniquely determined by parameters (G,ρ,ħ). Namely:
l_{cr}=ħ^{1/5}G^{-1/10}ρ^{-3/10}. #20
As expected, l_{cr} is increasing with increase of ħ and decreasing with increase of G and ρ. Particularly, at ρ=ρ₀, we get l_{cr,0}=ħ^{1/5}G^{-1/10}ρ₀^{-3/10}≈1. 498⋅10⁶cm≈15km. Corresponding time t_{cr}, when embryonic galaxies start to form, is determined by (19) with η_{cr}=ln(l_{cr,0}/a₀)≈-51. 7. The result is t_{cr}≈-187. 5by.So, it took 70.5 by of graviton production to initiate formation of galaxies. Corresponding critical mass m_{cr}=ρ₀l_{cr}³=ħ^{3/5}G^{=3/10}ρ₀^{1/10}≈ 8. 74⋅10⁻¹²g. Important nondimensional parameter of the theory is the critical number of gravitons N_{cr}=m_{cr}/m₀=ħ^{-2/5}G^{-4/5}ρ₀^{-2/5}c²=(c/u_{ħ,0})²≈ 1. 9⋅10⁵⁵. Here u_{ħ,0}=(ħG²ρ₀)^{1/5}≈ 6. 51⋅10⁻¹⁵cms⁻¹. This is a particular case of speed u_{ħ}=(ħG²ρ)^{1/5} of quantum gravitational waves in the condensate, which is uniquely determined by parameters (G,ρ,ħ). The obtained small value of u_{ħ,0} corresponds to small averaged mass density ρ₀. During formation of galaxies and interactions of stars, local ρ, potentially, can approach the Planck density ρ_{P}=c⁵/(ħG²) and local u_{ħ} can be comparable with c. Formula (20) can be applied to the blobs of dark matter in the halo of galaxies.
6 Creation of neutrinos from the background gravitons
Due to the collapsing mechanism, described in Ref. 7, some hot spots were developing during formation of galaxies. So, there is a necessity to get rid of an excessive energy. Apparently, photons were selected out of this necessity.
The next step in getting rid of excessive energy is selection of fermionic massive particles, which obey the Pauli exclusive principle and will run away from hot spots. Apparently, creation of new particles does not depend directly from gravity. We see it on example of photons, which are characterized only by parameters c and ħ. From these two parameters, which have dimensions [c]=LT⁻¹ and [ħ]=ML²T⁻¹, we can not construct a mass. That is why, the Standard Model can not predict absolute value of mass for observable particles. If G is included, than parameters (c,ħ,G) give uniquely the Planck mass m_{P}=(ħc/G)^{1/2}≈2.176⋅10⁻⁵gram, which is many orders heavier than observable particles (for example, mass of electron m_{e}≈9.11⋅10⁻²⁸gram).
In Qmoger theory, from parameters (c,ħ,ρ₀) we get unique mass:
m_{∗}=ρ₀^{1/4}(ħ/c)^{3/4}≈ 3. 13⋅10⁻³⁶gram≈1.76⋅10⁻³eV/c². #21
From the same parameters, we get unique length scale:
l_{∗}=(ħ/(cm_{∗}))=(((m_{∗})/(ρ₀)))^{1/3}=((ħ/(cρ₀)))^{1/4}≈10⁻²cm. #22
The obtained scale l_{∗} corresponds to the Compton wavelength of a particle with mass of background matter occupying volume of size l_{∗}. This indicates a mechanism of formation new particles from the background matter. We associate the obtained mass (21) with the first and the lightest massive fermionic particle created from the background condensate. The best candidate for that role from the observable particles is neutrino. Indeed, m_{∗} satisfies the experimental upper limit for neutrinos ∼4⋅10⁻²eV/c² [17]. Taking into account that m_{∗} is obtained from dimensional analysis, a moderate numerical factor is expected. The time scale:
t_{∗}=((ħ/(c⁵ρ₀)))^{1/4}≈3.3⋅10⁻¹³s #23
can be associated with formation and acceleration (c/t_{∗}≈8.46⋅10²²cms⁻²) of neutrino, as well as to the neutrino oscillations (transformation between three flavours) [17]. The physics of these oscillations can be related to interaction of neutrino with the background condensate of ultralight gravitons. The averaged number of gravitons interacting with such neutrino can be estimated by N_{∗}=m_{∗}/m₀=N_{cr}^{5/8}≈10³⁰. Below we will estimate the electric dipole moments (EDM) of both gravitons and neutrinos, which can be a significant factor of interactions. During its flight, neutrino can create some disturbances in the background condensate and temporary carry along coherent groups of gravitons, perhaps, in a form of vortex ring. This will influence the effective mass and the flavor of neutrino [17]. This an example of interface between dark and ordinary matter (Idom), introduced in context of explanation of the phenomena of subjective experiences (qualia) [18] (see also section 9). Note, that in frames of the Standard Model, the stability of all three neutrinos (v_{e},ν_{μ},ν_{τ}) was a long-time puzzle. In Qmoger, stability of the first-generation particles (neutrinos), produced by the background condensate, is natural.
7 Electric dipole moment of graviton and neutrino.
The baryonic asymmetry of the universe ( prevalence of matter over antimatter ) can be explained if gravitons have nonzero electric dipole moment (EDM). Indeed, EDM of primary particles can break the reflection symmetry and give advantage to matter over antimatter. It will also help to explain synthesis of some particles from the dipolar quantum condensate. Additionally, EDM of gravitons helps to explain qualia [18] and brightens the dark sector of matter (see below).
Technically, it is more simple to estimate EDM of neutrino, because, as explained above, properties of neutrino do not affected directly by G. From parameters (c,ħ,ρ₀) we get unique expression for EDM of neutrino or similar first-generation particle, produced by the the background condensate:
d_{∗}=(((ħ³c)/(ρ₀)))^{1/2}≈5.8⋅10⁼¹¹g^{1/2}cm^{5/2}s⁻¹≈ 0.12ecm. #24
For gravitons we have additional parameter G. The general expression for EDM of graviton, from dimensional argument, can be written in the form: d₀=d_{∗}F(m₀/m_{∗}) with arbitrary function F. If we assume that EDM of graviton is proportional to its mass, than d₀∼1.2⋅10⁻²⁹ecm. In Ref. 4, 5 it was suggested that d₀∼m₀^{1/2}l_{P}^{3/2}c∼2⋅10⁻⁷²gram^{1/2}cm^{1/2}s⁻¹, where l_{P} =(ħG/c³)^{1/2}≈1.6⋅10⁻³⁷cm is the Planck length. In any case, d₀ is very small and conventional telescopes can not see gravitons (dark matter). It also very difficult to detect gravitons in the supercollider or in any high energy machine. But, in section 9 we consider a novel approach to study gravitons.
8 Vacumo
The solution (10) of the partial differential equations (3, 4) is valid under condition a(t)≥l_{P}, which corresponds to sufficiently smooth space-time. In frames of Qmoger, the time t₁ of the beginning of the universe is naturally determined by equation a(t₁)=l_{P}. From (10), we get t₁≈-327by [19, 4, 5]. So, there was t_{g}-t₁ ≈68by of feeding the infant universe before it was able to produce gravitons. The time t₁ corresponds to the mass of the universe M₁=ρ₀l_{P}³≈10⁻¹²⁸gram (recall, that the mass of graviton m₀≈4.6⋅10⁻⁶⁷gram). That results suggest existence of particles or quasiparticles with energy smaller than E₀≈2. 61⋅10⁻³⁴eV. If such particle has the rest mass, it is smaller than m₀. Any such particle we call vacumo. Apparently, the universe is feeding by vacumos, which than transform into gravitons. Vacumos also can play a role of mediators between gravitons and ordinary matter, particularly, in formation of neutrinos (see above).
In Ref. 10 is was argued, that dark matter particle (which we now call gravitons, see above) consists of a pair of massive photons. They do not have to be ordinary photons, but photon-like particles. That is consistent with EDM of gravitons (see above).
9 Qualia
In our subjective experiences (qualia) we can actually see and feel the collective effects of the background gravitons [18]. The acting potentials of neurons [20], apparently, create gaps and coherent patterns in the condensate of gravitons. Remarkably, these interfaces between dark and ordinary matter (Idom) in cases of neutrino and qualia are similar. Note, that length scale (22) is of the same order as the size of the neuron cluster, which can produce sufficiently rich qualia. The necessary for qualia huge number of degrees of freedom is supplied by the indicated in section 6 number of gravitons N_{∗}≈10³⁰. It will not be surprising if oscillating neutrinos, which interact with gravitons (see above), play a role in qualia along with the acting potentials of neurons. At the same time, artificial sources of neutrino in a laboratory setting, potentially, can be used for healing and stimulation of the brain. By manipulating with acting potentials and quantifying qualia responses, we can open a new window into the dark sector of matter.
10 Conclusions
This paper presents a beginning of a new type of theory, in which the laws of nature are evolving along with the evolution of the universe. The laws of nature are approximate in connection with the feeding of the universe by the vacuum and because of the indicated above instabilities (see also below). Particularly, the conservation of energy emerged when there was already enough energy, so, that additional feeding has small effect on the local balance of energy. The universe is an open (non-Hamiltonian) system. The evolution of the universe was started with selection of the (3+1)-dimensional space-time and gravity, as a stable situation for a beginning. Then came the quantum condensate of gravitons for an additional stabilization. When this condensate becomes gravitationally unstable, the production of ordinary matter (photons, neutrino and more heavy particles) was selected as a relieve from excessive energy in hot spots. From the human point of view, the highest present achievement of the developing universe, of course, is qualia, which was produced by the interface between gravitons and ordinary matter.
In future, we can combine the Standard model and the Quantum Field Theory with Qmoger. This will definitely open new directions of research in physics.
¹⁾Note, that Newton and Einstein did not use the Lagrangian, the Hamiltonian and the variational principle. Unfortunately, these days the physical and common sense are often replaced by the variational principle. We can blame textbooks, which are convenient to base on the variational principle. In my opinion, it can lead theoretical physics astray. The non-Hamiltonian Qmoger theory with its seeping gravitons, apart from correcting cosmology, could also help to correct some of deficiencies in the Quantum Field Theory, particularly, the inequivalent representations [11]. Indeed, the active background can eliminate unstable representations of reality.
References
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[17] https://en.wikipedia.org/wiki/Neutrino
[18] E. A. Novikov, Gravicommunication, subjectivity and quantum entanglement, NeuroQuantology, v. 14, issue 4, 677-682 (2016).
[19] E. A. Novikov, Age of the universe and more, J. of Cosmology v. 25, 13442-13452 (2015).
[20] https://en.wikipedia.org/wiki/Action_potential.
[Figure]
Fig.1. Comparison of exact analytical solution (2) with results of two observational projects and with some parametric models (details in Ref. 10, 14). Here z=a₀/a-1 is the redshift, m-M is the distance module as function of z, m and M are apparent and absolute magnitudes of the source correspondingly. The observations are model-independent.
PDF file at viXra:1712.0004

MORTAL THIRST FOR LOVE. СМЕРТЕЛЬНАЯ ЖАЖДА ЛЮБВИ
As in the Cosmos, in our blood Как и в Космосе, в нашей крови
there is a mortal thirst for love! есть смертельная жажда любви!
Евгений Новиков, 13 Ноября 2017, Сан Диего, США.

EMERGENCE OF THE LAWS OF NATURE
Evgeny A. Novikov
University of California - San Diego, BioCircuits Institute, La Jolla, CA 92093 -0328; E-mail: enovikov@ucsd.edu
"All theory, dear friend, is gray, but the golden tree of life springs ever green".
Johann Wolfgang von Goethe.
Abstract
Based on the quantum modification of the general relativity (Qmoger), supported by the cosmic data without fitting, it is suggested that the vacuum is producing matter with random properties. The stable types of matter survive, the unstable absorbed by the vacuum. All laws of nature are emergent and approximate, including the conservation of energy.

HOLY COSMIC CONDENSATE OF ULTRALIGHT GRAVITONS WITH ELECTRIC DIPOLE MOMENT
Evgeny A. Novikov
University of California - San Diego, BioCircuits Institute, La Jolla, CA 92093 -0328; E-mail: enovikov@ucsd.edu
Abstract
Quantum modification of general relativity (Qmoger) is supported by cosmic data (without fitting). Qmoger equations consist of Einstein equations with two additional terms responsible for production/absorption of matter. In Qmoger cosmology there was no Big Bang and matter is continuously producing by the Vacuum. Particularly, production of the ultralight gravitons with possible tiny electric dipole moment was started about 284 billion years ago. Quantum effects dominate interaction of these particles and they form the quantum condensate. Under influence of gravitation, the condensate is forming galaxies and producing ordinary matter, including photons. As one important result of this activity, it recently created us, the people, and continues to support us. Particularly, our subjective experiences (qualia) are a result of an interaction between the background condensate and the neural system of the brain. The action potentials of neural system create traps and coherent dynamic patterns in the dipolar condensate. So, qualia are graviton-based, which can open new directions of research in biology and medicine. At the same time, a specialized study of qualia can open a new window into the dark sector of matter. The Qmoger theory explains why most of the ordinary particles are fermions, predicts the mass of neutrino (in accord with the experimental bound) and explained their oscillations (between three flavors) in terms of interaction with the background condensate. The achievements of the Standard Model and the Quantum Field Theory can be combined with the Qmoger theory.
Key words: cosmology with continuous production of energy, ultralight gravitons with tiny electric dipole moment, biophysics, qualia.
1. Introduction.
The level of a civilization, to a high degree, is determined by its cosmology. To the oldest question - Who we are?- this article, based on the described below quantum modification of general relativity (Qmoger), gives the answer: "We are creatures of the cosmic quantum condensate of ultralight dipolar gravitons - particles, which started to seep from the Vacuum about 284 billion years ago". How does it sound? Let us take it slowly. First of all, in Qmoger the matter/energy is produced continuously. This is in contrast with the conventional Big Bang cosmology [1] with singular release of energy about 13.7 billion years ago. Some problems with Big Bang theory are described in Ref. 1, 2. Additional critical analysis of the old cosmology and main results of new cosmology, supported by cosmic data (without fitting, see below), were presented in Ref. 3, 4 and references there. In the new cosmology, our universe was quietly born in the infinite past (mathematically speaking). At those times there was nothing but the Vacuum with small quantum fluctuations. Than, about 327 billion years (by) ago an embryonic universe was born with size about Planck length l_{P}=(G_{∗}ħc )^{1/2}∼1.6×10⁻³⁷cm ( G_{∗}=Gc⁻⁴, G - gravitation constant, c - speed of light, ħ - Planck constant) and mass:
M₁=ρ₀l_{P}³≈10⁻¹²⁸gram, #1
where ρ₀ is the current averaged mass density of the universe. At this stage, one may naturally ask two questions: why 327 by and why ρ₀? Qmoger theory answer these and other questions ( even more important). 2. Quantum modification of general relativity (Qmoger).
Qmoger equations are presented in the Appendix along with derivation of exact analytical solution:
a(τ)=a₀exp[H₀τ-2π(τ/L_{∗})²], L_{∗}=(G_{∗}ε₀)^{-1/2}, τ=ct. #2
Here a(τ) is the time dependent averaged size of the universe (scale factor), subscript 0 indicate initial (current) value, ε₀=ρ₀c² is the energy density, H₀ is Hubble constant, divided by c - current value of H(τ)=a/a, where dot indicate differentiation with respect to τ. Solution (2) corresponds to constant energy density ε(τ)=ε₀. That is why we have ρ₀ in (1). According to WMAP data [5], we use ρ₀≈2.6⋅10⁻³⁰gram⋅cm⁻³, which includes dark and ordinary matter, but not the so called dark energy, which we do not need in our theory.
In fact, problems with dark energy (ridiculously small cosmological constant) were a major motivation for the Qmoger theory, presented originally in Ref. 6. This work was presided by invention of new type of fluid, namely, dynamics of distributed sources/sinks [7,8], which in turn where presided by exact analytical solution of the (1+1)-dimensional Newtonian gravitation [9]. I love to simplify things and to get analytical solutions (second motivation for Qmoger). In Ref. 9 it was shown, particularly, that Newtonian gravitation leads to singularities in spacial dimensions 1 and 2. So, the third motivation for Qmoger was to get rid of singularities, particularly, from Big Bang - see, how smooth is function (2).
Solution (2) formally gives beginning of the universe at infinite past with a(-∞)=0. But, (2) is the solution of the differential equations for the time-space metric, which is supposed to be smooth. So, in frame of the Qmoger theory, it seems natural to start with size l_{P}, when we can expect formation of smooth spacetime metric. Putting a(τ)=l_{P} in (2), we get equation for τ. Solution of this equation, corresponding to the past, gives 327 by [10, 4].
According to (2), evolution of the universe is determined by characteristic physical scale L_{∗}≈76 billion light years (bly), which is comparable with the size of the visible universe a₀≈46.5 bly. Remarkably, H₀L_{∗}≈2.6. The temporal scale H₀⁻¹ and the eternal scale L_{∗} are of the same order because currently a(τ) is relatively close to its maximum. Indeed, after reaching maximum a_{max}≈1,32a₀ at t_{max}≈12.6by from now, a(τ) decreases and a(∞)=0 (see details in Ref. 4).
It seems natural to assume that mass m₀ of the dark matter particles (DMP), which fill out the universe, is determined by condition that the relativistic uncertainty of partial position [11] (or Compton wavelength) ħ/m₀c is of order of L_{∗}. This gives:
m₀=ħ(G_{∗}ρ₀)^{1/2}∼5⋅10⁻⁶⁷gram. #3
These particles we call gravitons, because only gravity field was used in the theory. In this paper we will not compare such definition with many definitions and use of gravitons in the literature [12]. Let us only stress, that Qmoger theory is not Hamiltonian ( see also Appendix). Gravitons in this theory are not virtual, but real particles with small, but finite mass (3) [compare with electron mass m_{e}∼9⋅10⁻²⁹gram] and, possibly, with some electromagnetic properties (see below).
Concentration of gravitons n and characteristic scale l (averaged distance between them) are:
n=ρ₀/m₀∼0.5⋅10³⁷cm⁻³, l=n^{-1/3}∼0,27⋅10⁻¹²cm. #4
The mass of the embryonic universe (1) indicates, that there are particles (or quasiparticles) with masses smaller than the mass of graviton m₀. We will call such particles vacumos (see also below). It seems that a metrical part of the Vacuum is feeding the universe with vacumos, not unlike an ovary is feeding a fruit, and becomes a part of it. The supply of vacumos may come from an external part of the Vacuum, which do not need to be equipped with a metric. To determine when universe started to produce gravitons, we put a(τ)=l into (2), solve equation for τ and got the result: 284 by ago [10, 4]. So, it took 43 by of "incubation" to accommodate universe for production of gravitons.
Formula (2) does not have any fitting parameters and shows good quantitative agreement with cosmological observations (SnIa, SDSS-BAO and reduction of acceleration of the expanding Universe [13]). Comparison with observational data was made in Refs. 14, 15, 3 , see also Fig.1 below. We can not expect better agreement of a global solution with data obtained from particular galaxies, evolution of which does not have to be synchronized. Effect of local bangs in galaxies on scale factor is described in terms of isenthalpic process (w≡ρc²+p=w₀, where p is pressure) [16]. Let us stress, solution (2) avoids major longtime controversies [critical density of the universe, dark energy (ridiculously small cosmological constant) and inflation].
The ultralight gravitons have huge concentration (4). The "ordinary" matter (OM) in this theory was synthesized from dark matter in galaxies [3, 4]. Averaged concentration (4) is not only enormous, but also constant. It means, that these particles somehow communicate with each other and polarize vacuum in order to maintain averaged distance l (4). Remember, that we are dealing with unusual fluid [7, 8]. The thermal de Brogle wavelength [17] for the temperature of the universe T≈2.73K is many orders bigger than l: ħc(lk_{B}T)⁻¹≈3⋅10¹¹ (k_{B} - Boltzmann constant). This estimate is for massless particles. For nonrelativistic gravitons with mass m₀ the relation is ħl⁻¹(m₀k_{B}T)^{-1/2}≈7⋅10¹³. So, the quantum effects, such as Bose-Einstein condensate, can dominate, even for high temperature.
In the areas of gravitational condensation (future galaxies) the density was much higher than (4). With certain critical density, we can expect local bangs (recall Ref. 9) with multiple collisions and formation of new particles in some sort of "natural selection". During the steady and stable expansion of the universe, the ordinary matter (OM) was synthesized in this way, probably, starting with light particles. Particularly, the production of neutrinos from the background gravitons and the oscillation (between the three flavors) are described recently [18, 19] in frames of Qmoger. The estimated mass m_{∗}=ρ₀^{1/4}(ħ/c)^{3/4}≈ 3. 13⋅10⁻³⁶gram≈1.76⋅10⁻³eV/c² [18, 19] corresponds to the experimental bound [20]. The neutrino oscillations are example of an interface between dark and ordinary matter (Idom). Another and possibly related example of Idom is our subjective experiences (see below). The introduced above vacumos could be expected to participate in both these phenomena.
The background condensate of gravitons, being under pressure in galaxies, is forming new particles and expels them from the hot places. This explains why most of the ordinary particles are fermions, obeying the Pauly exclusion principle. This also can lead to an additional acceleration of ordinary matter relative to the background condensate, which will be considered in detail in future work. These processes were accompanied by radiation, which is reflected in cosmic microwave background (CMB). The eqilibrium character of CMB and the small global curvature of the universe are naturally explained by the large amount of time available for the evolution. Some peculiarities of CMB can be associated with synthesis of various particles in expanding universe. Particularly, the observed anisotropy of CMB can be connected with nonsynchronous processes in galaxies.
In context of the type of evolution, which is described by exact solution (2), what we call ordinary matter is, in fact, an exotic matter, which was synthesized from gravitons and, so far, constitute about 15% of the total mass of the universe ( standard 4% corresponds to inclusion of dark energy). Taking into account the history of the universe, the vacumos (see above), the indicated below spectrum of mass and mediators between gravitons and OM ( perhaps, connected with vacumos), we can not be sure that graviton is elementary particle. Moreover, we can not be sure that gravitons obeys all the rules of the conventional quantum theory. It is possible, that gravitons and mediators produce some quantum effects for "ordinary" matter (see new interpretation of quantum theory [21]).
3. Electric dipole moment of gravitons.
The baryonic asymmetry of the universe ( prevalence of matter over antimatter ) can be explained if gravitons have nonzero electric dipole moment (EDM). Indeed, EDM of primary particles can break the reflection symmetry and give advantage to matter over antimatter. It will also help to explain synthesis of some particles from the dipolar quantum condensate. Additionally, EDM of gravitons helps to explain qualia [22] and brightens the dark sector of matter (see also next section and Appendix). In a mean time, simple estimation can be made in frame of Qmoger. From mass m₀ (3), l_{P} and c we have unique expression for EDM:
d∼m₀^{1/2}l_{P}^{3/2}c∼2×10⁻⁷²gram^{1/2}cm^{5/2}sec⁻¹ #5
There is also scale l₀=m₀Gc⁻²∼4⋅10⁻⁹⁵cm, which is much smaller than l_{P}. So, we have small nondimensional parameter ν=l₀/l_{P}∼2.5⋅10⁻⁶² and more general formula d=m₀^{1/2}l_{P}^{3/2}cN(ν). We will get (5), assuming that N(0) is finite. Using ν, we have spectrum of mass: m(α)=m₀ν^{α}. Scale l₀ and vacumos (for α>0) can be related not only to the early evolution, including indicated above "incubation" period, but also to mediators. Vacumos and mediators are potentially observable, particularly, in connection with the neutrino oscillations [18, 19] and qualia.
Let us note, that presented calculations of mass (3) and EDM (5), actually, do not require the full acceptance of the Qmoger theory. It is sufficient to accept, that ρ₀ is an important parameter.
4. Conclusions.
In the described theory we got that gravitons constitute omnipresent background in the universe. As a result of gravitation, from that background emerged OM. The indicated above mediators can be produced spontaneously, or during collisions. The "plasma" of gravitons and mediators produces ordinary matter, including photons. So, we got interface between dark and ordinary matter (Idom). Such interface very likely exists not only in cosmos, but everywhere, including our body and our brain¹⁾. A model of Idom is described in Ref. 22. From that model it follows that our subjective experiences (qualia) are manifestations of Idom and can be used as a natural detector of interaction between gravitons and ordinary matter. The typical action potentials (say, 30mV ) [23] of neural system can easily create traps and coherent dynamic patterns in the dipolar condensate with obtained above values of particle mass (3) and EDM (5). The necessary for qualia enormous number of degrees of freedom is supplied by huge concentration of gravitons (4). So, our subjective experiences are graviton-based. This can open new directions of research in biology and medicine. It also justify the given above answer to the big question: Who we are? - at the present level of understanding.
That answer suggest a specialized study of qualia, which can shed some light on the nature of the dipolar condensate of gravitons. The EDM (5) is small and existing telescopes do not see gravitons (dark matter). It seems also difficult to observe gravitons in the supercollider and in other high-energy machines. But we actually see the collective effects (condensate) of gravitons in qualia. By manipulating with action potentials of the neuron system and quantifying qualia responses, we can open a new window into the dark sector of matter. The neutrino oscillations are also connected to Idom [18, 19] and investigation of both phenomena (experimentally and in terms of Qmoger) can be mutually beneficial.
Appendix: Qmoger equations.
Qmoger equations, introduced in Ref. 6 and discussed in more detail in Ref. 4, differ from the Einstein equations by two additional terms responsible for production/absorption of matter by the vacuum:
R_{i}^{k}-(1/2)δ_{i}^{k}R=8πG_{∗}T_{i}^{k}+λ_{N}δ_{i}^{k},T_{i}^{k}=wu_{i}u^{k}-δ_{i}^{k}p,w=ε+p, #A1
λ_{N}=λ₀+β((dσ)/(ds))+γσ²,σ=((∂u^{k})/(∂x^{k}))+(1/(2g))((dg)/(ds)),(d/(ds))=u^{k}(∂/(∂x^{k})) #A2
Here R_{i}^{k} is the curvature tensor, p, ε and w are pressure, energy density and enthalpy density, respectively, G_{∗}=Gc⁻⁴(G- gravitational constant, c- speed of light), u^{k} - components of velocity (summation over repeated indexes is assumed from 0 to 3, x⁰=τ=ct), λ₀ is the cosmological constant (which we will put zero), σ is the covariant divergency, β and γ are nondimensional parameters (with particular choice β=2γ=2/3, see below) and g is the determinant of the metric tensor. With β=γ=0 we recover the classical equations of GR. Let us note that curvature terms in lhs of (A1) and additional terms dσ/ds and σ² all contain second order (or square of first order) derivatives of metric tensor, which make these terms compatible. The importance of σ also follows from the fact that it is the only dynamic characteristic of media, which enters into the balance of the proper number density of particles n: dn/ds+σn=q, where q is the rate of particle production (or absorption) by the vacuum. So, if n is constant (see the exact analytical solution (A7) below) or changing slowly, than the σ-effect is, certainly, very important in quantum cosmology. The σ-terms were introduces [6] with such physical argumentation on base of previous works [7-9]. Later, in the case β=2γ, equations (A1, A2) were derived from the variational principle by simply replacing the cosmological constant λ₀ (in the Lagrangian) by λ=λ₀-γσ²[14]. Indeed, the variation of ∫d⁴x(-g)^{1/2}σ² with respect to the metric tensor produces the two σ-terms in (A1, A2) [14]. But, the system is not Hamiltonian, the vacuum is feeding the universe, so, the standard approach is not appropriate²⁾. Parameters (β,γ), generally, depend on the equation of state [16].
Some exact analytical solutions of equations (A1, A2) where obtained in Ref. 6. On the basis of these solutions, it was concluded that the effect of spacetime stretching (σ) explains the accelerated expansion of the universe and for negative σ (collapse) the same effect can prevent formation of singularity. Equations (A1, A2) reproduce Newtonian gravitation in the nonrelativistic asymptotic, but gravitational waves can propagate with speed, which is not necessary equal to speed of light [14]. This give us a hint that gravitons may have finite mass.
The natural next step was quantitative comparison with cosmological data and choice of parameters β and γ. Let us consider equations for the scale factor a(τ) in homogeneous isotropic universe, derived from (A1, A2) by standard procedure [Eq. (8,9) in Ref. 6, or Eq. (3, 4) in Ref. 4]:
(2-3β)(a/a)+(1+3β-9γ)((a/a))²+(k/(a²))-λ₀=-8πG_{∗}p, #A3
-β(a/a)+(1+β-3γ)((a/a))²+(k/(a²))-((λ₀)/3)=((8π)/3)G_{∗}ε. #A4
Here points indicate differentiation over τ, the discrete curvature parameter k=0,+1,-1 corresponds to flat, closed and open universe, respectively.
With indicated in Ref. 6 unique choice β=2γ=2/3, these equations take simple form:
(k/(a²))=λ₀-8πG_{∗}p, #A5
H=((3k)/(2a²))-((λ₀)/2)-4πG_{∗}ε, H≡(a/a) #A6
From (A5) with λ₀=0, we see that sign of curvature is opposite to sign of pressure. From observations we know that global curvature is close to zero. So, the dust approximation (p=0 ) is natural for this theory with λ₀=0 and β=2γ=2/3.
In the dust approximation with λ₀=0,k=0, two special cases for system (A3, A4) have been indicated [6]: 1) for β=2/3 and γ≠1/3 stationary solution exist; 2) for β=2γ the global energy is conserved, except for β=2γ=2/3. The choice β=2γ=2/3 is exceptional and in the dust approximation with λ₀=0,k=0, equation (A5) is identity and from (A6) we have exact analytical Gaussian solution:
a(τ)=a₀exp[H₀τ-2π(τ/L_{∗})²],L_{∗}=(G_{∗}ε₀)^{-1/2} #A7
Here subscript 0 indicate present epoch (τ=0) and H₀ is the Hubble constant. In the analogous solution, obtained in [14], instead of ε₀ was ε₀+λ₀/8πG_{∗}, for generality.
Solution (A7) corresponds to continuous and metric-affecting production of dark matter (DM) particles out of vacuum, with its density ρ₀=ε₀c⁻² being retain constant during the expansion of spatially flat universe. In this solution there is no critical density of the universe, which is a kind of relief.
The solution (A7) is shown [14] to be globally stable in the regime of cosmological expansion until t_{max} about 12.6 billion years from now. After that time, the solution becomes unstable and characterizes the inverse process of dark matter particle absorption by the vacuum in the regime of contraction of the universe. More general class of solutions of Qmoger equations is presented in Ref. 4, 16.
In Qmoger equations we can have some extra terms (Qmoger+) to account for electromagnetic (EM) and other fields, but the presented above σ-terms seems to be unique. Inclusion of EM field in Qmoger is needed for problem of graviton-induced radiation from stars and hot planets (such as Jupiter and Saturn) [16], as well as for investigation of qualia [22 ]. At the same time, Qmoger with its seeping gravitons could lead to correction of some deficiencies in the Quantum Field Theory, particularly, the inequivalent representations [24]. Indeed, the active background can eliminate unstable representations of reality. In future, we can combine the achievements of the Standard model and the Quantum Field Theory with Qmoger. This will definitely open new directions of research in physics.
¹⁾ It did not escape my attention, that this approach has important philosophical consequences. Particularly, nonmaterial entities can be considered as interfaces (or collections of interfaces) between different types of matter. Also, the approach can be imbedded in a mathematical structure, similar to the category theory [25], with morphisms (see Ref. 22) and formalized interfaces, but that is another story.
²⁾Note, that Newton and Einstein did not use the Lagrangian and the variational principle. Unfortunately, these days the physical and common sense are often replaced by the variational principle. We can blame textbooks, which are convenient to base on the variational principle. In my opinion, it can lead theoretical physics astray.
References
[1] https://en.wikipedia.org/wiki/Big_Bang
[2] Steinhardt, Paul J. The inflation debate: Is the theory at heart of modern cosmology deeply flawed?, Scientific American, April; pp. 18-25 (2011).
[3] E. A. Novikov, Ultralight gravitons with tiny electric dipole moment are seeping from the vacuum, Modern Physics Letters A, 31, No. 15, 1650092 (5 pages) (2016).
[4] E. A. Novikov, Quantum modification of general relativity, Electr. J. Theoretical Physics, 13, No. 35, 79-90, (2016).
[5] https://map.gsfc.nasa.gov/
[6] E. A. Novikov, Vacuum response to cosmic stretching: accelerated universe and prevention of singularity arXiv:nlin/06080050.
[7] E. A. Novikov, Dynamics of distributed sources, Physics of Fluids 15, L65 (2003).
[8] E. A. Novikov, Distributed sources, accelerated universe and quantum entanglement, arXiv:nonlin.PS/0511040.
[9] E. A. Novikov, Nonlinear evolution of disturbances in (1+1)-dimensional universe, Zh. Exper. Teor. Fiz. 57, 938 (1969) [Sov. Phys. JETP. 30 (3), 512 (1970)]; arXiv:1001,3709 [physics.gen-ph].
[10] E. A. Novikov, Age of the universe and more, J. of Cosmology v. 25, 13442-13452 (2015).
[11] V. B. Berestetskii, E. M. Lifshitz & L. P. Pitaevskii, Quantum Electrodynamics, Pergamon press (1982).
[12] https://en.wikipedia.org/wiki/Graviton.
El-Nabulsi, Rami Ahmad, Gravitons in Fractional Action Cosmology, Int. J. Theor. Phys. 51 (2012) 3978. R. Casadio, A. Giugno, A. Giusti, Matter and gravitons in the gravitational collapse, Phys. Lett. B763 (2016) 337. C. de Pham, J. T. Deaskins, A. J. Tolley and S-Y. Zhot, Graviton mass bounds, Rev. Mod. Phys. 89 (2017), 025004. A. F. Zakharov, P. Jovanovicc, D. Borka and V. B. Jovanovic, Graviton mass trajectories of bright stars at the Galactic Center, J. Phys.: Conf. Ser. 798 (2017) 01081.
[13] A. Shfieloo, V. Sahni, & A. Starobinsky, Is cosmic acceleration slowing down?, Phys. Rev. D 80, 101301(R) (2009).
[14] S. G. Chefranov & E. A. Novikov, Hydrodynamical vacuum sources of dark matter self-generation without Big Bang, J. Exper. Theor. Phys., 111(5),731-743 (2010) [Zhur. Eksper. Theor. Fiz.,138(5), 830-843 (2010)]; arXiv:1012.0241v1 [gr-qc].
[15] E. A. Novikov & S Chefranov, A quiet cosmology and halo around the visible universe, J. of Cosmology 16, 6884 (2011).
[16] E. A. Novikov, Isenthalpic universe (submitted for publication).
[17] https://en.wikipedia.org/wiki/Thermal_de_Broglie_wavelength
[18] E. A. Novikov, Feeding the universe, quantum scaling and stable neutrinos (submitted for publication).
[19] E. A. Novikov, A possibility of brain stimulation by oscillating neutrinos (submitted for publication).
[20] https://en.wikipedia.org/wiki/Neutrino
[21] E. A. Novikov, Random shooting of entangled particles in vacuum, arXiv:0707.3299.
[22] E. A. Novikov, Gravicommunication, subjectivity and quantum entanglement, NeuroQuantology, v. 14, issue 4, 677-682 (2016). [24] https://plato.stanford.edu/entries/quantum-field-theory/#DefStaForQFT
[25] J. C. Baez and M. Stay, Topology, logic and computation: a Rosetta stone, arXiv:0903.0340
[Figure]
Fig.1. Comparison of exact analytical solution (2) with results of two observational projects and with some parametric models (details in Ref. 14, 15). Here z=a₀/a-1 is the redshift, m-M is the distance module as function of z, m and M are apparent and absolute magnitudes of the source correspondingly. The observations are model-independent.
Submitted for publication, posted at viXra:1709.0401

BRAIN STIMULATION WITH NEUTRINOS
Evgeny A. Novikov
University of California - San Diego, BioCircuits Institute, La Jolla, CA 92093 -0328; E-mail: enovikov@ucsd.edu
Abstract
A possibility of brain stimulation with neutrinos is discussed.
Recently, based on the quantum modification of general relativity (Qmoger) [1, 2], it was discovered [3-5] that phenomena of subjectivity (qualia) have something in common with oscillations of neutrinos - mutual transformations of the three flavors of neutrinos [6]. Both phenomena are examples of interface between the dark and the ordinary matter (Idom), introduced in Ref. 3.
The Compton wavelength of neutrino was estimated [4, 5]:
l_{∗}=(ħ/(cm_{∗}))≈10⁻²cm. #1
Here ħ is the Planck constant, c is the speed of light and m_{∗} is the mass of neutrino [4, 5]:
m_{∗}=ρ₀^{1/4}(ħ/c)^{3/4}≈ 3. 13⋅10⁻³⁶gram≈1.76⋅10⁻³eV/c². #2
We use the averaged mass density of the universe ρ₀≈2.6⋅10⁻³⁰gcm⁻³, which includes ordinary and dark matter. We do not include the controversial dark energy, which does not exist in Qmoger [1, 2]. The mass of neutrino satisfies the experimental bound [6].
The wavelength l_{∗} is comparable with the size of neuron cluster, which is expected to be capable of producing sufficiently rich qualia. Humans are continuously subjected to the neutrino showers from the sun and other cosmic sources [6]. Seemingly random jumps of our memory could be related to interaction with neutrinos. In any case, it will be interesting to study these interactions in a controlled laboratory setting by using artificial sources of neutrinos [6]. The possible gain, apart of the scientific inquire, is a new tool for healing and stimulation of the brain.
References
[1] E. A. Novikov, Ultralight gravitons with tiny electric dipole moment are seeping from the vacuum, Modern Physics Letters A, 31, No. 15, 1650092 (5 pages) (2016).
[2] E. A. Novikov, Quantum modification of general relativity, Electr. J. Theoretical Physics, 13, No. 35, 79-90, (2016)
[3] E. A. Novikov, Gravicommunication, subjectivity and quantum entanglement, NeuroQuantology, v. 14, issue 4, 677-682 (2016).
[4] E. A. Novikov, Feeding the universe, qualia and neutrino, submitted for publication, posted at viXra: 1708.0116.
[5] E. A. Novikov, Feeding the universe, quantum scaling and stable neutrino, submitted for publication, posted at viXra: 1708.0213.
[6] https://en.wikipedia.org/wiki/Neutrino

FEEDING THE UNIVERSE, QUANTUM SCALING AND STABLE NEUTRINOS
Evgeny A. Novikov
University of California - San Diego, BioCircuits Institute, La Jolla, CA 92093 -0328; E-mail: enovikov@ucsd.edu
Abstract
Based on the quantum modification of the general relativity (Qmoger), it is shown, that the Vacuum is continuously feeding the universe with ultralight particles (vacumo). Vacumos are transforming into more heavy (but still ultralight) gravitons, which form quantum condensate even for high temperature. The condensate, under gravitational pressure in galaxies, produces and expels from the hot places the first generation of "ordinary" massive fermions, which are identified with neutrinos. It explains the stability of all three neutrinos (a puzzle in the Standard Model). The mass of neutrino, estimated in terms of a new scaling in Qmoger, satisfies the experimental bound. The oscillations of neutrino are explained in terms of interaction with the background condensate of gravitons. The electric dipole moment of neutrino is also estimated. The situation with neutrinos is an example of interface between dark and ordinary matter (Idom), introduced before in explanation of the phenomena of subjectivity.
In the quantum modification of the general relativity (Qmoger), in contrast with the conventional Big Bang theory (BB) [1], the matter (energy) is continuously produced by the Vacuum. The Qmoger equations differs from the Einstein equations of the general relativity by two additional terms, responsible for production (absorption) of matter [2-4]. These works were presided by invention of a new type of fluid, namely the dynamics of distributed sources-sinks [5, 6], which, in turn was presided by exact analytical solution of the (1+1)-dimensional Newtonian gravitation [7]. Qmoger theory was motivated by many deficiencies of BB [1-4, 8]. The additional terms in Qmoger equations take into account the space-time divergency (stretching), the effect of which is comparable with the effect of the space-time curvature in the Einstein theory. The additional motivation of Qmoger is that the Standard Model [9], principally, can not predict absolute values of masses for observable particles, while Qmoger can do this (see below).
The simples situation with continuous production of matter from the Vacuum is when the averaged density of matter is constant: ρ=ρ₀. In more general situation [10] the averaged density of enthalpy is constant: w=ε+p=w₀, where ε=ρc² is the energy density, p is the pressure and c is the speed of light. The pressure can be high in stars. But the averaged pressure in the universe is small and the dust approximation (p=0) is useful in many situations. In this case, the main parameters in the Qmoger theory are: the gravitational constant G, c and ρ₀. From these parameters we have unique length scale:
L_{∗}=c(Gρ₀)^{-1/2} #1
We use value ρ₀≈2.6⋅10⁻³⁰gcm⁻³, which, according to WMAP, includes ordinary and dark matter. We do not include the dark energy, which does not exist in Qmoger (see below). (1) gives L_{∗}≈76 billion light years (bly) [3, 4], which is comparable with the current size of the visible universe a₀≈46.5 bly. Qmoger equations have corresponding exact analytical solution [11, 3, 4] for the scale factor a in homogeneous and isotropic universe:
a(τ)=a₀exp[H₀τ-2π(τ/L_{∗})²],τ=ct, #2
where H₀ is the Hubble constant, divided by c, which is the current value of function H(τ)=d(ln a)/dτ. Remarkably, L_{∗}H₀≈2.6. The temporal scale H₀⁻¹ and the eternal scale L_{∗} are of the same order because currently a(τ) is relatively close to its maximum (see below). In the isenthalpic case (w=w₀), which takes into account radiation [10], Qmoger equations have the same solution (2) with L_{w}=c²(Gw₀)^{-1/2}instead of L_{∗}. These two scales are very close because averaged pressure in small.
Solution (2) does not have any fitting parameters and is in good quantitative agreement with cosmic data [11, 3]. This solution eliminates major controversies - critical density of the universe, dark energy (cosmological constant) and inflation.
In nonrelativistic regime, Qmoger reproduces Newtonian dynamics, but the speed of the gravitational waves can be different from c [11]. This give us a hint, that gravitons have mass (unlike photon). With scale (1) we associate gravitons with mass m₀=ħ/(cL_{∗})∼0.5⋅10⁻⁶⁶gram and electric dipole moment (EDM) d₀∼m₀^{1/2}l_{P}^{3/2}c∼2⋅10⁻⁷²gram^{1/2}cm^{1/2}s⁻¹[3, 4], where l_{P} =(ħG/c³)^{1/2}≈1.6⋅10⁻³⁷cm is the Planck scale. EDM of background gravitons can explain the baryon asymmetry of the universe (prevalence of particles over antiparticles) in terms of breaking the reflection symmetry. It is shown [3, 4]], that such particles form quantum condensate even for high temperature. The concentration of particles n and characteristic scale are:
n=ρ₀/m₀≈5⋅10³⁶, l=n^{-1/3}≈2.7⋅10⁻¹³cm. #3
According to (2), the universe was born in the infinite past (a(-∞)=0) from small fluctuation. But, formula (2) is solution of Qmoger differential equations for the space-time metric, which is assumed to be smooth. The smooth metric we can expect only starting with condition a=l_{P}. It is natural to associate this condition with the beginning of the universe in frame of the Qmoger theory. From that condition, using (2), we get time [3, 4]: t₁≈-327 billion years. The mass of the embryonic universe can be estimated by M₁=ρ₀l_{P}³≈10⁻¹²⁸gram. This result suggest existence of particles (or quasiparticles) with much smaller mass than m₀ (see also below). Any such particle we will call vacumo. It seems reasonable to suggest, that Vacuum is feeding universe with vacumos.
The next important step in the evolution of the universe is the production of gravitons with indicated above mass m₀. The corresponding condition is: a=l. In this case, (2) gives [4] : t₂≈-284 billion years. So, it took about 43 billion years of nurturing the universe to accommodate it for production of gravitons. It seems natural, that the feeding comes from an external part of the Vacuum, which do not have to be equipped with a metric. The mature universe transforms vacumos into gravitons, which form the background quantum condensate. Size of the universe (2) riches the maximum a_{max}≈ 1. 32 a₀ at time t_{max}=(L_{∗}²H₀)/(4πc)≈ 12. 6 billion years. It was shown [11], that universe is globally stable during expansion (-∞t_{max}.
During formation of galaxies (in a manner described in Ref. 7), in stars and in hot planets (Jupiter, Saturn), the local density of matter becomes large and new "ordinary"particles (including photons) are synthesized. In these processes, instead of G, the Planck constant ħ becomes important. Note, that in the Standard Model [9], from parameters ħ and c one can not construct a mass, a length scale or such characteristics as EDM. So, Standard Model, principally, can not predict absolute values of masses for observable particles and corresponding scales. In Qmoger, from c, ħ and ρ₀, we now have unique scale:
l_{∗}=ħ^{1/4}(cρ₀)^{-1/4}≈10⁻²cm. #4
We can rewrite (3) in the form:
l_{∗}=(ħ/(cm_{∗})), m_{∗}=ρ₀l_{∗}³=ρ₀^{1/4}(ħ/c)^{3/4}≈ 3. 1326×10⁻³⁶gram≈1.76⋅10⁻³eV/c². #5
So, scale l_{∗} corresponds to the Compton wavelength of a particle with mass of background matter occupying volume of size l_{∗}. This indicates a mechanism of formation new particles from background gravitons. Mass m_{∗} is determined uniquely by the new scaling. Apparently, it is a typical mass of the first generation of "ordinary" massive particles, produced by indicated mechanism from the background condensate. It is easy to expel such particles from the hot places if they are fermions, obeying the Pauly exclusion principle. Among the experimentally observed particles, neutrino is the best candidate for being produced in this way. Indeed, mass m_{∗} corresponds to experimental bound for the mass of neutrino [12]. The time scale:
t_{∗}=(ħ/ρ₀)^{1/4}c^{-5/4}≈3.3⋅10⁻¹³s #6
could be associated with formation and acceleration (c/t_{∗}∼ 8. 46⋅10²²cms⁻²) of neutrino, as well to the neutrino oscillations [12]. The physics of these oscillations can be related to interaction of neutrino with the background condensate of described above ultralight dipolar gravitons. The averaged number of gravitons interacting with such neutrino can be estimated by N_{∗}=m_{∗}/m₀∼10³⁰. During a flight, neutrino can temporary carry along a coherent group of gravitons (perhaps, in a form of vortex ring). This can influence the effective mass and the flavor of neutrino [12]. The stability of all three neutrinos was unexplainable in frames of Standard Model. But, in frames of Qmoger, the stability seems natural for the first generation of particles, produced by the background gravitons. The new scaling also predict EDM for neutrino or similar particles:
d_{∗}=ħ^{3/4}c^{1/4}ρ₀^{-1/4}≈5. 8⋅10⁻¹¹gram^{1/2}cm^{5/2}s⁻¹, #7
which is much bigger than indicated above EDM of graviton. Note, that Qmoger with its seeping gravitons could also correct some deficiencies of the quantum field theory, such as inequivalent representations [13]. Indeed, the active background can eliminate unstable representation of reality.
The situation with neutrino is an example of interface between dark and ordinary matter (Idom), which was introduced in Ref. 14 in explanation of the phenomena of qualia ( subjective experiences). In future, we can combine the achievements of the Standard Model and the quantum field theory with Qmoger and new scaling. This will open new directions of research in physics and biology.
References
[1] https://en.wikipedia.org/wiki/Big_Bang
[2] E. A. Novikov, Vacuum response to cosmic stretching: accelerated universe and prevention of singularity arXiv:nlin/06080050.
[3] E. A. Novikov, Ultralight gravitons with tiny electric dipole moment are seeping from the vacuum, Modern Physics Letters A, 31, No. 15, 1650092 (5 pages) (2016).
[4] E. A. Novikov, Quantum modification of general relativity, Electr. J. Theoretical Physics, 13, No. 35, 79-90, (2016).
[5] E. A. Novikov, Dynamics of distributed sources, Physics of Fluids 15, L65 (2003).
[6] E. A. Novikov, Distributed sources, accelerated universe and quantum entanglement, arXiv:nonlin.PS/0511040.
[7] E. A. Novikov, Nonlinear evolution of disturbances in (1+1)-dimensional universe, Zh. Exper. Teor. Fiz. 57, 938 (1969) [Sov. Phys. JETP. 30 (3), 512 (1970)]; arXiv:1001,3709 [physics.gen-ph].
[8] Steinhardt, Paul J. The inflation debate: Is the theory at heart of modern cosmology deeply flawed?, Scientific American, April; pp. 18-25 (2011).
[9] https://en.wikipedia.org/wiki/Standard_Model
[10] E. A. Novikov, Isenthalpic universe (submitted for publication)
[11] S. G. Chefranov & E. A. Novikov, Hydrodynamical vacuum sources of dark matter self-generation without Bing Bang, J. Exper. Theor. Phys., 111(5),731-743 (2010) [Zhur. Eksper. Theor. Fiz.,138(5), 830-843 (2010)]; arXiv:1012.0241v1 [gr-qc].
[12] https://en.wikipedia.org/wiki/Neutrino
[13] https://plato.stanford.edu/entries/quantum-field-theory/#DefStaForQFT
[14] E. A. Novikov, Gravicommunication, subjectivity and quantum entanglement, NeuroQuantology, v. 14, issue 4, 677-682 (2016).