Modeling the Past Hypothesis: A Mechanical Cosmology

TL;DR

This paper introduces a mechanical cosmology model to address the paradox of low initial entropy in the universe despite early thermal equilibrium, providing new insights into the statistical mechanics of cosmological expansion.

Contribution

It constructs a well-defined mechanical model that reproduces key features of big-bang cosmology and offers a framework to compute time-dependent entropies related to the past hypothesis.

Findings

Model reproduces standard cosmological features

Provides a method to compute evolving coarse-grained entropy

Offers insights into the entropy paradox in cosmology

Abstract

There is a paradox in the standard model of cosmology. How can matter in the early universe have been in thermal equilibrium, indicating maximum entropy, but the initial state also have been low entropy (the "past hypothesis"), so as to underpin the second law of thermodynamics? The problem has been highly contested, with the only consensus being that gravity plays a role in the story, but with the exact mechanism undecided. In this paper, we construct a well-defined mechanical model to study this paradox. We show how it reproduces the salient features of standard big-bang cosmology with surprising success, and we use it to produce novel results on the statistical mechanics of a gas in an expanding universe. We conclude with a discussion of potential uses of the model, including the explicit computation of the time-dependent coarse-grained entropies needed to investigate the past hypothesis.