Initial Conditions for Defining an Arrow of Time at the start of Inflation?

Recently, Beckwith asked [1]if the following could occur, [ ] 3 T S T N E S ∝ → − ≡ μ by setting the chemical potential 0 → μ with initial entropy 5 10 ~ S at the beginning of inflation . Conventional discussions of the arrow of time states that as the Universe grows its temperature drops, which leaves less energy available to perform useful work in the future than was available in the past. Thus the Universe itself has a well-defined thermodynamic arrow of time. The problem of the initial configuration of the arrow of time, however, is not brought up. This paper is to initiate how to set up a well defined initial starting point for the arrow of time. Specifically re setting the degrees of freedom of about 120 100 ~ − ∗ g [2] of the electro weak era, to 1000 ~ ∗ g at the onset of inflation [1] , may permit


I. INTRODUCTION
Recently, Beckwith asked [1]if the following could occur, at the beginning of inflation .Conventional discussions of the arrow of time states that as the Universe grows its temperature drops, which leaves less energy available to perform useful work in the future than was available in the past.Thus the Universe itself has a well-defined thermodynamic arrow of time.The problem of the initial configuration of the arrow of time, however, is not brought up.This paper is to initiate how to set up a well defined initial starting point for the arrow of time.Specifically re setting the degrees of freedom of about

A. What can be said initially about usual arrow of time formulations of early cosmology ?
Usual treatments of the arrow of time, i.e. the onset of entropy .The discussion below makes the point that expansion of the universe in itself does not 'grow' entropy The entropy density s of a radiation field of temperature T is s ~ T 3 .The entropy S in a given comoving volume V is S = sV .Since the commoving volume V increases as the universe expands, we have V ~ R 3 .And since the temperature of the microwave background goes down as the universe expands: T ~ 1/R, we have the result that the entropy of a given comoving volume of given space S ~ R -3 * R 3 = constant.Thus the expansion of the universe by itself is not responsible for any entropy increase.There is no heat exchange between different parts of the universe.The expansion is adiabatic and isentropic: d S expansion = 0. I.e. a process has to be initiated in order to start entropy production This discussion above is to emphasize the importance of an initial process for the onset and the growth of entropy .We will initiate candidates for making sense of the following datum To measure entropy in cosmology we can count photons.If the number of photons in a given volume of the universe is N, then the entropy of that volume is S ~ kN where k is called here Boltzmann's constant Note that Y. Jack Ng. has [3] , from a very different stand point derived n S ~based upon string theory derived ideas , with n a 'particle' count , which in Y. Jack Ng's procedure is based upon the number of dark matter candidates in a given region of phase space..Y.Jack Ng's idea was partly based upon the idea of quantum ' infinite ' statistics, and a partition function, details of which will be in Appendix A below.This counting procedure is different from traditional notions .To paraphrase them, one can state that "The reason why entropy is increasing is because there are stars in that "box" ( unit of phase space used for counting contributions to entropy).Hydrogen fuses to helium and nuclear energy is transformed into heat."I.e. the traditional notion would be akin to heat production due to, initially start BBN nucleosynthesis, and then, frankly , star production/ nuclear burning.I.e.one would need to have nuclear processes to initiate heat production.This idea of heat production is actually similar to setting 3 T S ∝ , with heat production due to either BBN/ hydrogen burning leading to an increase in temperature, T. In this manuscript, we make use of, if , with n an initial 'quantum unit' count in phase space of Planckian dimensions, where 5 10 S at the beginning of inflation.Let us now look at how to initiate such a counting algorithm if one is looking at , say, highly energized gravitons , initially, as part of a counting 'algorithm' .As suggested earlier by Beckwith [4], gravitons may have contributed to the re-acceleration of the universe one billion years ago.Here, we are making use of refining the following estimates.In what follows, we will have even stricter bounds upon the energy value (as well as the mass) of the graviton based upon the geometry of the quantum bounce, with a radii of the quantum bounce on the order of GeV l E planck Planck eff

A1 . Estimating the size of contribution to energy in
Then, taking note of this , one is obtaining having a scaled entropy of

A II. The electro weak generation regime of space time for Entropy and early universe Graviton production before eletro weak transitions
A typical value and relationship between an inflaton potential [ ] φ V , and a hubble parameter value, H is  [6] and denotes that the electro weak transition was a 'strongly first order phase transition') then one can write , by conventional theory that Here, the factor put in, of * g ~ is the number of degrees of freedom.Kolb and Turner [2] Should the degrees of freedom hold, for temperatures much greater than * T , and with 1000 ~≈ * g at the onset of inflation, for temperatures, rising up to , say T ~ 10 19 GeV, from initially a very low level, pre inflation, then this may be enough to explain how and why certain particle may arise in a nucleated state, without necessarily being transferred from a prior to a present universe.Furthermore, if one assumes that H. de La Vega, in conversations with the author in Colmo, Italy, 2009 [7].flatly ruled out having 1000 ~≈ * g initially.What will be presented here will be a justification for taking this step which H. de La Vega says is not measurable and possible.The author points to, among other things, the Wheeler de Witt derivation for a wave function of the universe, as given by M. Morris [8] (1989) in perturbative super space, with no restriction on the degrees of freedom.While the WdW style of stellar evolution is now out of fashion, something akin to obtaining an initial 'wavefunction of the universe' as given in his Eq.(3.1) of his article is , by the authors view, necessary, to make sense out of initial conditions appropriate for n T S 3 ∝ when 1000 ~≈ * g .The count, n, would be in terms of a procedure brought up by both Beckwith, [1] and Mukhanov [9] on page 82 of his book leading to a Bogoluybov particle number density of becoming exponentially large, where 1 η is a time evolution factor, which we can set , with β some numerical multiplicative factor for the Planck interval of time Planck t [1], [9] [ ] If so, then one can also ask if there is a linkage between the initial conditions, as pertinent to early inflation, and Beckwith's model of re acceleration of the universe one billion years ago.

B. Linkage between the initial onset of inflation, and re acceleration of the universe one billion years ago ?
The following is speculative, and if confirmed through additional research would be a major step toward a cosmological linkage between initial inflation, and re acceleration of the universe one billion years ago [2] .Look at A. Yurov's [10] double inflation hypothesis, i.e.Claim: there exist one emergent complex scalar field Φ and that its evolution in both initial inflation and re acceleration is linked.I.e. he states that this scalar field would.accountfor both 1st and 2nd inflation • Potential in both cases chaotic inflation of the type [10] (1.8) The "mass" term would be, then, as Beckwith 1,2 understands it, for early universe versions of the Friedman equation (1.9) Furthermore, its bound would be specified by having (1.10)The term, l would be an artifact of five dimensional space time, as provided in a metric as given by Maarten's [11] as (1.11)The 2 nd scalar fields as Yurov [10] writes them contributing to the 2 nd inflation, which Beckwith represents [2] is (1.12)And (1.13)As Beckwith sees it, making a full linkage between Yurov's formalism [10] for double inflation, Beckwith's re acceleration graphics [2] , and initial inflationary dynamics, as referenced by obtaining would be to make the following relations between Yurov's [10] versions of the Friedman equations, and what Beckwith [2] did, (1.14)As well as having: The left hand side of both Eq (1.14) and Eq (1.15) are Yurov's [10], and the right hand side of both Eqn.(1.14) and Eq (1.15) above are Beckwith's adaptation [1] of modification of Maarten's brane theory [11] work which was used in part to obtain the re acceleration of the universe graphics Beckwith obtained [2] a, i.e. the behavior of massive gravitons one billion years ago to mimic DE in terms of the re acceleration parameter IN any case, the following would be needed to be verified to make the linkage .(1.16) i.e. that the potential energy, V, of initial inflation is initially over shadowed by the contributions of the Friedman equation, H, at the onset of inflation.
We should note, that the potential energy as stated would be assuming that Eq. (1.16) has consistency with Eq. (1.5), for very large temperatures

C . Conclusions
A way to obtain traces of information exchange , from prior to present universe cycles is finding a linkage between information and entropy.If such a parameterization can be found and analyzed, then Seth Lloyd's [12] shorthand for entropy, could be utilized as a way to represent information which can be transferred from a prior to the present universe .The question to ask, if does Eq.(1.17) permit a linkage of gravitons as information carriers, and can there be a linkage of information, in terms of the appearance of gravitons in the time interval of, say Planck t t < < 0 either by vacuum nucleation of gravitons / information packets Appropriate values / inputs into ρ are being considered along the lines of graviton mass/ contributions along the lines brought up in this paper already An alternative to Ea. (1.7) if one sees no way of implementing what Ng. suggested via his infinite quantum statistics [3] would be to look at thermal inputs from a prior to the present universe, as suggested by L. Glinka [13,14] [ ] ( ) ( ) As well as, if 75 .0 h ( ) For looking at Our guess is as follows.That the thermal flux from a prior to the present universe may account for up to 10 10 bits of information.These could be transferred from a prior universe to our present , and that there could be , perhaps Whichever model we can come up with that does this is the one we need to follow, experimentally.And it gives us hope in confirming if or not we can eventually analyze the growth of structure in the initial phases of quantum nucleation of emergent space time [18] .
of inflation.This entails, as we will detail , having increased number of degrees of freedom, initially, with re setting the degrees of freedom of of inflation, I.e.what will be examined will be the feasibility of the following:

1 )
For looking at the onset of creation, with a bounce; if we look at planck

.
One needs, then to consider, if the energy per given graviton is, if a frequency grams is taken when applied to Eq. (1.2) above.
4) Also, if we look at the temperature * T occurring about the time of the Electro weak transition , if * ≤ T T when c T T = * was a critical value, (of which we can write v(Tc) /Tc >1 , where v(Tc) denotes the Higgs vacuum expectation value at the critical temperature Tc., i.e. v(Tc)/Tc >1 according to C. Balazc et al (2005) even if T ~ 1019 GeV >> * T , then there is the possibility that 3 could also hold, if there was in pre inflationary states very LOW initial temperatures, which rapidly built up in an interval of time, as could be

π
If we take into consideration having final a a ~, then Eq. (1.14) above will, in most cases be approximately

T 180 10 1 ) 10 2) 10 10 3 )
e. close to the final value of today's scale value, Filling in/ choosing between either implementation of Eq. 1.7, or Eq.1.10 will be what the author is attempting to do in the foreseeable future.I.e. if one can use[3] GeV in about a time interval during the onset of inflation, for the beginning of the arrow of time, in cosmology.Beckwith views determining if the degrees of freedom initially could go as high as 1000 ~≈ * g or even higher even if T ~ 10 19 GeV as essential in determining the role of 3 T S ∝ as , as temperatures go from an initial low point, to T ~ 10 19 GeV for understanding the role of thermal heat transfer in the arrow of time issue.Note, very importantly, any coupling between Eq. (1.5) and Eq.(1.16) probably require that there be no initially low temperature behavior , pre inflation, prior to the rise of temperature the that of the Quantum Planck Temperature of ~ 10 19 GeVC1.Open Question, do we have a match up with Smoot's Ercole Challonge table?Guess as to possible outcomes presentedIn a colloquium presentation done by Dr. Smoot in Paris[16] (2007); he alluded to the following information theory constructions which bear consideration as to how much is transferred between a prior to the present universe in terms of information 'bits'.0)Physically observable bits of information possibly in presentUniverse -Holographic principle allowed states in the evolution / development of the Universe -120 Initially available states given to us to work with at the onset of the inflationary era-Observable bits of information present due to quantum / statistical fluctuations -8 10 information temporarily suppressed during the initial changing of fermion states of matter to a bosonic phase of matter right at the onset of the big bang itself .'Thenafter the degrees of freedom dramatically drops during the beginning of the descent of temperature to at least three orders of magnitude less, as we move out from an initial red