What if the value of entropy was just zero at the beginning? What if the spatial potential and the inertial energy just formed at the BB? The entropy would have increased ever since... Do we have any strong hints at something else?

The value of entropy is not defined. Only defined is the change in entropy. Correct? So, one can not say what the percent of entropy ((deltaS/S) *100%) has changed at all, if the S is large enough. Am I right? If no, then what is S today? Is it S=67.975? Or 45.753?

@Dimitri, i think that the change dS is what determines the entropy of the ensuing universe -- the vacuum stays with its own undefined entropy of the vacuum. in other words it ain't deltaS/Svac that matters. so according to the second law S today would only be greater than dS. 

regarding the vacuum temperature let's assume that the bubble is a black hole of a Schwarzchild radius of the order of a Planck length. we therefore have dS|BH ~ k = 10−23 J/K. this determines a very high temperature, Tvac = 1033 K. does this make sense?  

What if the value of entropy was just zero at the beginning? What if the spatial potential and the inertial energy just formed at the BB? The entropy would have increased ever since... Do we have any strong hints at something else?

If the Universe was created from nothing at the Big  Bang (negative gravitational energy then paying for all positive energy) then the entropy must have been zero initially. There is only one way to have nothing, so by Boltzmann's relation S = k ln OMEGA = k ln 1 = 0 initially.

@RJ Low, yes, i am aware of this hypothesis. in my calculation, i am not making use of the curvature whatsoever although it is a warped bubble. any suggestions on how to incorporate it? maybe, as surface tension?  

Consult papers by Lineweaver, Egan for an investigation of this question:

 http://www.mso.anu.edu.au/~charley/papers/Chapter22Lineweaver.pdf

 http://www.mso.anu.edu.au/~charley/papers/EganLineweaverApJOnline.pdf

 http://www.mso.anu.edu.au/~charley/papers/LineweaverEganParisv2.pdf

I do agree with explanation given by Dmitri Martila

May be this article help you

https://arxiv.org/pdf/0712.0029

Asher,

I asked a similar question in April (see enclosed link) with completely different answers compared to those given to your question. Probably because the question started with a "number of microstates" point of view view (statistical entropy) rather than the basic thermodynamic equation for 𝛿U as you do !

Difficult to have a definite answer … Probably because anybody has a firm idea of what is entropy but much less of how to apply it to the big bang of the universe (with all the uncertainties and speculations around it) ?

https://www.researchgate.net/post/What_was_the_value_of_the_entropy_of_the_Universe_shortly_after_the_Big_Bang

i think that adding a potential of the form ħc/r where r is on the Planck scale is going to change Tvac dramatically. also will have to refer to the free energy.  

Since dS=dU/T+PdV/T-dG/T,  here G=\sum{_j}μ{_j}n{_j} is Gibbs free energy, i think you need to explain the term Gibbs free energy, and this is an equation of the equilibrium thermodynamics.

if “has a negative constant pressure”, this pressure is not only the thermal/heat  pressure, you need to distinguish the sources of the two partial pressures, one comes from thermal motion, another one comes from interactions,  these two partial pressures have different signs, and i don’t understand, if  the initial state “has a negative constant pressure”,  the state will be non-equilibrium,  then can we use the equation of the equilibrium state?

There is an interesting point of view, the laws of physics that dominate the universe now was created by the big bang,  so i don’t know whether these laws can also be used in the initial state of the big bang.

Asher,

Remi Cornwall : "I think what we are all struggling with is the universality of the 2nd law, meaning that we expect the entropy of the universe to increase, yet having to contend with a very high temperature (but small volume) at the beginning".

Remi Cornwall : "Therefore, I would say that the entropy at the start of the big bang was zero ....".

I agree with Remi Cornwall. The entropy at the start of the big bang was probably zero or (close to zero), e.g. because the universe was probably in a very singular micro-state. And in line with standard hot big bang cosmology the temperature is thought to have been extremely high at the beginning.

So, in spite of the fact that I agree with Tang Suye that you use a basic equation for equilibrium thermodynamics (which is questionable to describe the beginning of the universe), and as your thinking comes to evaluate Tvac (is it high or low ?), I'd answer that the temperature (not necessarily Tvac) having been extremely high at the beginning, the entropy would have probably been extremely low : zero or close to zero (confirming the statistical approach).    

Before the separation of gravity, the entropy was zero. Immediately after gravity separates, it is as given below. In the following PQG model (see eqns. 85 & 86) the value of the entropy of the Universe shortly after the Big Bang is S = 196.6 x 10^(-23) J/K which corresponds to W = 7.46383 x 10^(61) and each microstate having planck energy level which corresponds to macrostate energy level of 1.823x10^(81) GeV which is the total energy of the universe at present epoch including CDM and dark energy.

Article Periodic quantum gravity and cosmology