A Breathing Universe is Consistent

TL;DR

This paper explores a toy universe with exotic topology, demonstrating that quantum field content can lead to consistent semi-classical equations with entropy reversals, linking thermodynamic and cosmological arrows of time.

Contribution

It introduces a specific quantum field setup in an $S^1 \times S^3$ universe that ensures consistency of semi-classical equations with periodic time, supporting entropy reversal cycles.

Findings

Semi-classical Friedman equations are consistent with periodic time in the toy universe.

Entropy reversals occur during each cycle, aligning thermodynamic and cosmological arrows of time.

The model supports a universe with exotic topology and cyclic behavior.

Abstract

We consider a toy FRW universe with the exotic topology $S^1 \times S^3$. We show that for a specific choice of quantum field content, the semi-classical Friedman equations are consistent with temporal periodicity as required by the $S^1$ timelike factor. A straightforward consequence is that entropy reversals occur during each cycle, consistent with Hawking's proposed connection between the thermodynamic and cosmological arrows of time.