Several routes to determining entropy generation in the early universe

We analyze how entropy could be generated via a semi classical argument as well as by multiple braneanti brane combinations leading to an initial soliton-instanton formation. The supposition is that the two different types of methods give similar initial conditions for entropy and information/ computational bits of information in the initial universe. We close then with observations we think are pertinent to entropy increase . This is linkable to a table of computational bits as presented by Smoot in 2007. PACS 96.50.Ry, 98.80.-k, 98.80.Cq, 98.80.Bp


Introduction
We wish to present two alternative routes to generation of entropy. One is strictly a semi classical argument, linked to the exponential of early universe entropy being proportional to the spatial integral of energy minus an interaction between particles or clumps 1 . The other is a brane world summation of brane and anti brane components 2 which are in a very small space time geometry of no less than several orders of magnitude larger than Planck length, cubed. This second result is orthodox brane theory for the formation of an instanton, but it is remarkable that this same argument as given in the IUCAA meeting pre supposes the same increase in minimum geometrical length scale which the more semi classical argument gives.
We then will mention in passing how to form a five dimensional instanton in pre inflation space 3 , and then the datum of a worm hole bridge between a prior to our present universe. This will be put in the context of an embedding of the instanton in pre inflation space, and its connections with the model given above of brane world instanton formation due to branes and anti branes. This among other thing has consequences to black hole physics and entropy via brane and anti branes 4 which we will mention as an area to be explored later.
The intersection of all these arguments does several things simultaneously. First, it establishes a minimum criteria for forming entropy. It secondly links entropy to instanton formation. We also mention in passing an argument linked to changes in energy density states, at the start of inflation with an increase as of entropy which would account for the dramatic growth of entropy after what we refer to as a causal discontinuity barrier breaking the instanton of energy density transmitted from a prior to a present universe.
The main point of the article which is presented toward the end is that there are bench marks as to information based complexity of cosmological evolution. This was presented by Smoot in the Challonge symposia of August 2007 5 . The main point in the end is that analyzing the particulars of cosmological models which purport to analyze initial phases of the big bang, and inputs of the big bang would be well advised as to try to answer or in part match the computational complexity bench marks Smoot is offering in the table reproduced at the end of this document.

Semi classical models of entropy generation
Kolb and Turner 6 have a temperature T related entropy density which can be treated as being written as This pre supposes when we do it that we are able to state a total entropy as the entropy density times space time volume 4 In this situation we are writing for initial conditions with a temperature K T 32 10 ≈ for the initiation of quantum effects for quantum gravity as given by Weinberg (1972) 7 We will examine if or not the following is actually true in terms of time, i.e. can we write 2 ) / ( P t t I = ? This is assuming that the density 9 energy vacuum T − Λ ≡0 0 ρ which is initially enormous, and which will be due in terms of a transfer of energy density from a prior universe to our present universe, which will be elaborated upon later in this document. We can if we take the absolute value of Eqn. (3) and (2) above get for small volume values good estimates as to the relative volume of the phase space in early universe cosmology where Eqn. (2) and Eqn. (3) are congruent with each other. For our purposes, we will take time as greater than (or equal) to a Planck time interval, in line with the temperature dependence of entropy density mentioned in Eqn. (1) above.
We can compare this with Thanu Padamanadan's treatment of entropy 1 which is with regards to micro canonical ensemble as defined via we re scale it as being of order unity, and 87 10 N particles, and we re scale where we choose 4 V , and where we assume Eqn (2) and Eqn.
(3) are equivalent and we assume that there is grounds for writing ρ π , we can shed light on if or not it is still feasible to treat entropy, with 87 10 N as a micro canonical ensemble phenomena, which we claim has implications for the formation of an instanton in early universe cosmology. Frankly we would want, in early universe cosmology that we have ( 2 1 4 ρ , but not by too much, so we can form an instanton.

Brane world picture of early universe entropy formation
This is adapted from a lecture given at the ICGC-07 conference by Samir Mathur 2 . The supposition is that branes and anti branes form the working component of an instanton. Which is part of what has been developed.
I.e. look at the case, first of massless radiation, and then we obtain for D space time dimensions, and E the general energy The question now becomes how do we go about defining what the necessary volume is re scaled via a quantum gravity changing of how to measure gravitational lengths which are for the threshold of quantum gravity .
Traditionally the bench marking has been via the Planck length . This re scaling of the minimum length needed for the importance of quantum gravity effects showing up in a grid of space time resolves, as information paradox of black hole physics. So far we have merely been working with a typical string gas model for entropy. Now, let us add in a supposition for N ( branes and anti branes to put in an instanton structure as to how we look at the entropy. Gilad Lifschytz 4 in 2004 codified thermalization equations of the black hole which was recovered from the model of branes and anti-branes, and in lieu of assuming an anti brane is merely in this situation the charge conjugate of say a Dp brane wrote an entropy along the lines of modifying Eqn. (5) above to read This has when we do it Total E as in Eqn. (5) above, and proportional to the cosmological vacuum energy parameter. Of course, in string theory, the energy is also defined via Our claim is that this very specific value of entropy for Eqn. ( 1 0 ) Furthermore we also claim that the interaction of the branes and anti branes will form an instanton structure, which is implicit in the treatment outlined in Eqn. (7) , and that the numerical counting given in Eqn (9) Leading to solving for E as follows

Comparing different models for how one can input thermalradiation energy.
Begin first with looking at different value of the cosmological vacuum energy parameters, in four and five dimensions 9 .
( ) in contrast with the more traditional four dimensional version of the same, minus the minus sign of the brane world theory version The five dimensional version is actually connected with Brane theory, and higher dimensions, whereas the four dimensional is linked to more traditional De Sitter space time geometry, as given by Park 10 ( 1 5 ) This is such that If one looks at the range of allowed upper bounds of the cosmological constant, we have that the difference between what Barvinsky 11 (2006) recently predicted, and Park (2003) [ ] If we have an order of magnitude equivalence between such representations, we can talk about a quantum regime of gravity which is consistent with regards to fluctuations in energy and also in the growth of entropy. We will use an order of magnitude estimate as to presenting what the vacuum energy should be in the neighborhood of Planck time in the advent of nucleation of a new universe

First principles argument as to large scale values of the absolute magnitude of the cosmological vacuum energy
Look at an argument provided by Thanu Padmanabhan 12   l , or at most 100 or so times larger ? Contemporary big bang theories imply this. I.e. a very high level of thermal energy. We need to ask if this is something which could be transferred from a prior universe , i.e. could there be a pop up nucleation effect , i.e. emergent space time? Appendix 1 gives a way for this to occur. We will now examine a mechanism which would allow for this to happen. It involves transfer of energy from a prior to the present universe.

Worm hole transition from a prior to the present universe.
To model this, we use results from Crowell 14 This assume that the cosmological vacuum energy parameter has a temperature dependence as outlined by Park (2003) As a wave functional solution to a Wheeler De Witt equation bridging two space times. This solution bridging two space times is similar to that being made between these two space times with 'instantaneous' transfer of thermal heat ,as given by Crowell 14

Conclusion. Match up with Smoot's table
In a colloquium presentation done by Dr. Smoot in Paris 15 (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 present
Universe -180 10 1) Holographic principle allowed states in the evolution / development of the Universe -120 10 2) Initially available states given to us to work with at the onset of the inflationary era- 10 10 3) Observable bits of information present due to quantum / statistical fluctuations - 8

10
Our guess is as follows. That the thermal flux so implied by the existence of a worm hole accounts for perhaps 10 10 bits of information. These could be transferred via a worm hole solution from a prior universe to our present , and that there could be , perhaps 120 10 minus 10 10 bytes of information temporarily suppressed during the initial bozonification phase of matter right at the onset of the big bang itself .
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 17 . We also need to consider the datum so referenced as to the irregularities as to the cooling down phase of inflation, as mentioned by Sakar, 18 which is below "Quasi-DeSitter spacetime during inflation has no "lumpiness" -it is necessarily very smooth. Nevertheless one can generate structure in the spectrum of quantum fluctuations originating from inflation by disturbing the slow-roll of the inflaton -in our model this happens because other fields to which the inflaton couples through gravity undergo symmetry breaking phase transitions as the universe cools during inflation" We intend to model this better, and to come up with experiments better than what Ruutu et al 17 . came up for early universe structure model paradigms.