Thermo/hydro visualization of the Cosmos

[Mordred]

Anyone that has paid attention to my numerous posts, know that I am a self taught, wannabe cosmologist. I've studied numerous cosmology related articles including, high energy particle physics, perfect fluid and quantum metrics related to Cosmology in the form of the FLRW metrics.
As a self taught Cosmologist I wish to clarify a self visualization of a cosmological behavior/characteristic.

As I relate to cosmology the universe as of 10^-43 sec started out at a hot dense state of unknown size and origin, (numerous theories apply to prior). Naturally this hot dense state will want to disperse to a lower energy state per quanta. (suitable volume unit to describe a lowest possible energy state). As we all know in thermodynamics and pressure laws, a high pressure or temperature region will disperse to the limits of the container to the lowest possible energy state. In terms of cosmology any region of higher energy mass density will desire to reach that lower/evenly distributed energy state.( Makes you wonder in regards of the cosmological constant as merely a pressure/dispersion rate of combined particles/energy forms of that process). Gravity however runs counter to the tendency for energy-mass to evenly distribute, in many ways can be described as localized/positive pressure that for whatever reasons wishes to condense energy-mass. (space-time geometry?) Much of the universes history can be described in the terms of thermo/pressure dispersion vs localized gravity coupled with the dispersion rates, mean free path and distinguishable separation of the particles involved at a specific time period in the universes thermodymanic history

Opinions and discussions of that viewpoint welcome

 

[mfb]

The universe is not some mass in a larger volume where it could disperse into. Spacetime is part of the universe. In the early universe, there was also no spatial variation where thermodynamics could move stuff around.

In general relativity, pressure actually slows expansion.

 

[Mordred]

you raised valid points, some of what I wrote is misleading in terms of the container aspect. For one there is no universe wall lol. This article better describes what I was poorly doing in terms of pressure dispersion usually most articles deal with ideal gas in a container or a closed system, in terms of a closed system that is one without outside influences, the universe has no outside influences so would qualify a closed system. I found point number 2 of particular interest as I commonly calculated the temperature with the inverse of the scale factor.

thermodynamics in Cosmology

http://arxiv.org/abs/0708.2962

the ideal gas laws as they apply in cosmology according to this paper obeys the following rules

1. In cosmology, the thermodynamic process is isentropic, it is always at the state of maximum entropy.
2. The temperature of the Universe varies as (22), it does not simply decrease in proportion to the inverse of scale factor
3)The equation of state (34) slightly differs from the usual result of thermodynamics. By (32)
and (34), we find the EOSP=P(ρ) satisfying the following increasing and causal condition

now the ideal gas laws has the following requirements.

1) there are no intermolecular forces between the molecules.
2) the volume of the gas is negligible compared to the volume of the container they occupy.
3) the interactions between the particles and the container is perfectly elastic (total kinetic energy is conserved).

equation of state for an ideal gas is given by pV=nRT

so how does one define rules 2 and 3 in terms of cosmology? or in terms that relate to what you described after all we use the ideal gas calculations in cosmology for a large variety of applications, some invoke energy-mass anistrophy barriers for localized effects but how is it applicable on the global? Thats the part I have trouble finding the answer to in my self research

The universe is not some mass in a larger volume where it could disperse into. Spacetime is part of the universe. In the early universe, there was also no spatial variation where thermodynamics could move stuff around.

In general relativity, pressure actually slows expansion.

 

[Mordred]

going further with the ideal gas laws

This law has the following important consequences:

1) If temperature and pressure are kept constant, then the volume of the gas is directly proportional to the number of molecules of gas.
2) If the temperature and volume remain constant, then the pressure of the gas changes is directly proportional to the number of molecules of gas present.
3) If the number of gas molecules and the temperature remain constant, then the pressure is inversely proportional to the volume.
4) If the temperature changes and the number of gas molecules are kept constant, then either pressure or volume (or both) will change in direct proportion to the temperature.

another important consideration is that the work done by pressure in an expanding fluid is done by its kinetic energy.

now looking at my cosmology textbook by Weinberg section 3.1 thermal history

looking at at temperature of 10¹¹ which according to th text is too cold for muon-antimuon and hadron-antihadron pairs to be produced in appreciable numbers.
in this circumstance he describes the collision rate of photons with electrons and other charged particles to be so much greater than the rate of expansion, and that the photons and charged particles are in thermal equilibrium.
However Griffiths particle physics text describes it better (at least in my humble opinion) in terms of a reduced mean free path due to the overall density. In other words photons cannot travel far due to collision caused by the excessive density.

The problem I have with Weinburg's description is that it implies a volume restriction, ie a container or finite universe. However Griffiths statement works regardless of volume (finite or infinite)

let's move past that lol. the rest of Weinburg's text has some interesting statements.

"The conditions of thermal equilibrium tells us that the entropy in a com-moving volume is fixed"

s(T)a³=constant.

the second law of thermodynamics says that any adiabatic change in a system of volume V produces a change in the entropy given by

d(s(T)V)=d\rho(T)V)+P(T)d/T

The problem I have with ideal gas laws usage in cosmology is still related to the 2nd and 3rd conditions

2) the volume of the gas is negligible compared to the volume of the container they occupy.
3) the interactions between the particles and the container is perfectly elastic (total kinetic energy is conserved).

Every formula he uses in a restricted mean free path, with no chemical interactions (although he implies that the volume of expansion is equivalent to the volume of the container)

going with his terminology

" the collision rate of photons with electrons and other charged particles to be so much greater than the rate of expansion, and that the photons and charged particles are in thermal equilibrium."

How does that work with conditons 2 and 3?

like I stated I need clarity on how to define ideal gas usage in cosmology lol

edit: unfortunately Scott Dodelson's modern Cosmology and Barbera Ryden's Introductory to Cosmology offer no assistance in this regard grrr,

 

[Mordred]

Found this handy article that covers what I was looking for, fills in the blanks on what I posted prior. in regards to Weinberg's text that I have.

http://www.wiese.itp.unibe.ch/lectures/universe.pdf

the section I was having trouble on is based on the section notes in this article covered in better detail in this article. in chapter 4 page 41. The Bose-Einstein and Dirac distribution section in Weinberg's was giving me hassle.

Unfortunately I can't post the Weinberg descriptions that were giving me problems. However the second article provided the missing metrics such as the Dirac-distributions and Bose-Einstein distributions. The combination of the two resources gave me a far better understanding of several aspects of the radiation dominant era prior to inflation. As well as after.