Friedmann Cosmology at T < 1 second

[Jorrie]

MTW section 27.7 states:

All estimates indicate that, except for the first few seconds of the life or the universe, the energy exchanged between radiation and matter was negligible compared to $\rho_m V$ and $\rho_r V$ individually (see section 28.1). Under these conditions equation (27.31) can be split into two parts: ...

It then proceeds to derive the relationships: $\rho_m a^3 =$ constant and $\rho_v a^4 =$ constant that pervect has shown before.

My question: does this mean one cannot push the basic Friedmann equations that were discussed so exhaustively in the locked thread 'Firedmann Fun' to a time before t ~ 1 second without gross errors?

If so, can someone please point to a fairly recent accessible paper showing how to deal with the time since inflation ended, up to 1 second? (Or better still, tell us how!)

 

[Wallace]

We don't precisely know the physics of the very very early universe and therefore do not know the equations of state of the energy components and any couplings between them. This info is needed to solve the Friedmann equations.

What would solving the Friedmann equations for T<1 second tell you anyway?

 

[Jorrie]

What would solving the Friedmann equations for T<1 second tell you anyway?

Thanks! Just thought it would be interesting to know how the densities evolved in that time bracket.

 

[jal]

Thanks! Just thought it would be interesting to know how the densities evolved in that time bracket.

Density determines the Schwarzschild radius.
It would be interesting to know how to get out of the black hole.
jal

 

[Jorrie]

Density determines the Schwarzschild radius.
It would be interesting to know how to get out of the black hole.
jal

I do not think the homogeneous universe as a whole ever had or will have a Schwarzschild radius, because it's a local inhomogeneity phenomenon.

 

[Chris Hillman]

Two corrections

Density determines the Schwarzschild radius.

Actually, mass, not density. Specifically, in the Schwarzschild vacuum solution, the event horizon is located at $r= 2 m$ in geometric units, where m is a parameter whose interpretation involves some discussion but which, to shorten a longer story, can be identified with "mass" of the (nonrotating) black hole modeled by this solution (or even better, by closely related solutions such as the Oppenheimer-Snyder model of a collapsing dust ball).

For various reasons (extensively discussed in well-known textbooks such as MTW), "density" can be tricky unless this refers to a scalar quantity (as in, a component of the stress-energy tensor, evaluted in a frame comoving with matter). Unfortunately you clearly can only be referring to a dubious notion of "density in the large", since the Schwarzschild vacuum is a vacuum solution.

It would be interesting to know how to get out of the black hole.
jal

http://www.math.ucr.edu/home/baez/physics/Relativity/BlackHoles/universe.html

In future, please try to perform some elementary fact checking before making unsupported claims.

 

[jal]

Thank you Chris Hillman.
That's what I'm trying to do... "fact checking"
jal
---------
I read your link
I'll quote "Perhaps the truth is even stranger. In other words, who knows?"
--------
I'm now reading ... trying to get more insight into everyones opinions.
http://arxiv.org/abs/0710.5721
The radiation equation of state and loop quantum gravity corrections
Authors: Martin Bojowald, Rupam Das
(Submitted on 30 Oct 2007)

 

[Chris Hillman]

Hi, jal, fair enough (and I appreciate the "thanks"!), but in future I suggest that you phrase such posts as "is the following correct?..." and "I know Wikipedia is unreliable but I happened to notice that article A in version V says in part... and wonder if this is correct".

 

[jal]

I wish I had had the occasion to become a "math kid" like you. I would have loved to spend time over a beer with you.

Sorry, out of time and got to run. Give me some insight on the bounce and black holes.
jal

 

[pervect]

MTW section 27.7 states:
It then proceeds to derive the relationships: $\rho_m a^3 =$ constant and $\rho_v a^4 =$ constant that pervect has shown before.

My question: does this mean one cannot push the basic Friedmann equations that were discussed so exhaustively in the locked thread 'Firedmann Fun' to a time before t ~ 1 second without gross errors?

If so, can someone please point to a fairly recent accessible paper showing how to deal with the time since inflation ended, up to 1 second? (Or better still, tell us how!)

My take on this is that while MTW has made this assumption that there is no interconversion of energy to matter, all that really *has* to be done is that both the dynamic and static Friedmann equations (which I called F1 and F2) must be satisfied. If both Friedmann equations are satisfied, the Einstein field equations will be satisfied.

I think that one first must pick a spatial curvature factor K, which specifies the spatial part of the geometry, and optionally chose some value for the cosmological constant $\Lambda$. Given this choice of K, one can subsequently specify any (well, actually any twice differentiable) function a(t) , and then use the Friedmann equations to compute rho(t) and P(t) from a(t) and K and $\Lambda$.

However, some of these solutions, for instance solutions with rho(t) < 0, are probably not physically interesting.

The trick is to find out which a(t) corresponds to a P(t) and rho(t) that has the desired relationship between P and rho.

The bigger trick is to figure out some theoretical grounds for some "equation of state" that one expects P and rho to satisfy.

 

[Chris Hillman]

I wish I had had the occasion to become a "math kid" like you. I would have loved to spend time over a beer with you.

Sorry, out of time and got to run. Give me some insight on the bounce and black holes.
jal

If I can find time, I might try to post something like "Intro to FRW", or "Survey of Cosmological Models", or "Signals in Spacetimes" in an appropriate forum. The application of superstring theory to cosmological speculations doesn't interest me as much as the application to enumerative geometry, however.