A Breathing Universe is Consistent

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.