# What about 2nd law of thermodynamics in Cyclic Universe Model?

## Main Question or Discussion Point

Not everyone likes the idea of Universe ​​created from a point singularity, so recently grows in popularity the cyclic model - that our Universe will finally collapse and use obtained momentum to bounce (so-called Big Bounce) and become the new Big Bang.
One might criticize that we "know" that universe expansion is accelerating. But it is believed to be pushed away by "dark energy", so accordingly to energy conservation, this strength should decrease with volume: like 1/R^3 ... while attracting gravity weakens like 1/R^2 and so should finally win - leading to collapse.

But it seems there is a problem with the second law of thermodynamics here - on one hand entropy is said to be always increasing toward the future, on the other Big Bangs should intuitively 'reset the situation' - start new entropy growth from minimum.
I wanted to collect the possible approaches to handling this problem and discuss them - here is a schematic picture of the basic ones I can think of (to be extended):

http://dl.dropbox.com/u/12405967/cyclicun.jpg [Broken]

The age of thermal death means that there are nearly no changes, because practically everything is in thermodynamical equilibrium, most of stars have extinguished.

1) The second law is sacred - succeeding Big Bangs have larger and larger entropy,
2) It is possible to break 2nd law, but only during the Great Bounce,
3) It is possible to break 2nd law in singularities like black holes - the Universe may be already in thermal death, while the entropy slowly "evaporates" with black holes (I think I've heard such concept in Penrose lecture in Cracow),
4) The second law of thermodynamics is not fundamental, but effective one - physics is fundamentally time/CPT symmetric. So Big Bounce is not only single Big Bang, but from time/CPT symmetry perspective, there is also second BB-like beginning of Universe reason-result chain in reverse time direction. The opposite evolutions would finally meet in the extremely long central thermal death age, which would probably destroy any low-entropic artifacts.

Personally,
I see 1) as a total nonsense - thermal death is near possible entropy maximum (like lg(N)).
Also 3) doesn't seem reasonable - hypothetical Hawking radiation is kind of thermal radiation - definitely not ordering energy (decreasing entropy), but rather equilibrating degrees of freedom - leading to thermalization of the Universe.
2) sounds worth considering - physics doesn't like discontinuities, but Big Bounce is kind of special - crushes everything, resetting the system.
And 4) seems the most reasonable, but requires accepting that thermodynamical time arrow is not fundamental principle, but statistical effect of e.g. low entropic BB-like situation: where/when everything is localized in small region.

Assuming our universe will eventually collapse, which thermodynamical scenario seems most reasonable? Why?
Perhaps above list requires expansion?
Did Universe started in a point, or maybe something ends - something begins?

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bapowell
Not everyone likes the idea of Universe ​​created from a point singularity, so recently grows in popularity the cyclic model - that our Universe will finally collapse and use obtained momentum to bounce (so-called Big Bounce) and become the new Big Bang.
One might criticize that we "know" that universe expansion is accelerating. But it is believed to be pushed away by "dark energy", so accordingly to energy conservation, this strength should decrease with volume: like 1/R^3 ... while attracting gravity weakens like 1/R^2 and so should finally win - leading to collapse.
Except that's not what Einstein's equations say will happen. The energy density associated with the accelerated expansion does not follow a 1/R^2 law of gravitational attraction, and it doesn't redshift as 1/R^3 (that's how the energy density of ordinary, non-relativistic matter evolves). No, dark energy is an especially unusual substance. In the limit that the dark energy is the cosmological constant, the energy density is constant, and yes, a naive application of energy conservation comes up with a surprising violation. But, energy is not strictly conserved in general relativity -- stress-energy is.

bapowell,
from one side, what if it is not "the biggest Einstein's mistake": cosmological constant, but a real energy density...
What energy? For example we directly observe 2.7K EM microwave background, which bounces from all matter, pushing everything away.
It is definitely not enough to explain the observed expansion (basing on undermined belief that we understand supernovas), but we have also other interactions and corresponding fields: weak, strong, gravitational. There is some nonzero interaction between these fields, so from thermodynamical point of view, their degrees of freedom could thermalize through these billions of years near this 2.7K - these noises would be difficult to directly observe, but maybe together would be enough to explain the expansion...

From the other side, I don't think we understand the Universe enough to be really certain of infinite expansion or collapse, especially that observations suggest that we are close to the boundary between them. The most precise tests of GRT confirmed only some its approximation (gravitomagnetism) - higher order terms of GRT are still just an assumption...

Maybe we can just assume the collapse here and try to answer fundamental thermodynamical questions, like what would be entropy in such Big Collapse?

bapowell
$$\dot{\rho} = -3H\rho(1+w)$$
where $\rho$ is the energy density, $H=\dot{a}/{a}$ is the Hubble parameter (with $a(t)$ the scale factor), and $w=p/\rho$ is the "equation of state parameter". Solving this equation for $\rho$ gives
$$\rho \propto a^{-3(1+w)}$$
Now, $w$ depends on the matter content; for the sake of illustration, assume that only a single component dominates. In this case, non-relativistic matter (pressureless dust) gives $w=0$, relativistic matter (radiation) gives $w=1/3$, and the cosmological constant has $w=-1$. The first two give decelerating universes, and so these are not dominant forms of energy in today's universe. The cosmological constant, and more generally any form of matter with $w< -1/3$ leads to an accelerating universe. These more general equations of state with $-1 \leq w \leq -1/3$ are termed "dark energy". You can plug these into the above expression to see how $\rho$ varies as the universe expands.