Bill Alsept started a thread raising the general question---do cosmic models with regularly repeating big bangs conflict with thermodynamics' 2nd Law? (The law to the effect that, where it can be defined, entropy does not decrease, or does so only by rare accident, at irregular intervals if at all.)(adsbygoogle = window.adsbygoogle || []).push({});

The original thread kept getting off track. It's hard for people to stay focused on the central issue which in cosmology isgeometricentropy. So I'll start this to consider just that question for a specific cosmic model: the LQC bounce version of the big bang.

According to bounce cosmology, the universe we see may have resulted from the collapse of one not greatly different from ours in a rough overall sense (except that distances were contracting instead of expanding). When the geometric law of gravity (GR) is replaced by a quantum version one finds that quantum effects make gravity repel at extreme densities. Computer simulations then show this causing a collapsing universe to rebound, and produce something which, like the conventional cosmo model, gives good agreement with observation.

Basically the bounce just reproduces the standard big bang model, but without a singularity.

The issue that immediately comes up is geometric entropy. The gravitational field is the geometry of the universe (curvature, dynamically changing distances...). One wants to be able to define the entropy of the gravitational field. Geometric entropy is a major player in the overall entropy picture.

Towards the end of collapse, things are highly clumped with lots of black holes, intuitively the geo-entropy is very high.

By contrast, in the early stages of expansion, geometry is smooth and even, stuff has not begun to condense into clumps---space is filled with nearly uniform hot gas. Intuitively, the geo-entropy is very low.

This intuition, that nice-smooth-even geometry has low entropy and crumpled-warty-pimply geometry has high entropy is based on our experience of gravity as attractive. Because it is attractive, matter always tends to clump, and form stars, galaxies, clouds, clusters, black holes...etc. Clumping makes geo-warts and geo-dimples.

This gives an OK intuition about geometric entropy as long as gravity is attractive. So it works up to a point.

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# Loop bounce and geometric entropy (re: Bill A's question)

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