Entropy of Contracting Universe in Cyclic Cosmology

TL;DR

This paper investigates the entropy of the contracting phase in a cyclic universe model with phantom dark energy, concluding that the entropy is effectively zero if the dark energy equation of state parameter is less than -1, thus addressing the entropy problem.

Contribution

It provides a detailed analysis of the contracting universe's entropy in a cyclic cosmology with phantom dark energy, showing entropy can be zero under certain conditions.

Findings

Entropy of contracting universe is zero if dark energy parameter ω < -1.

Presence of at most a single photon with infinitesimal energy after turnaround.

Time until turnaround is at least 100 billion years based on current bounds.

Abstract

Following up a recent proposal \cite{BF} for a cyclic model based on phantom dark energy, we examine the content of the contracting universe (cu) and its entropy $S_{cu}$. We find that beyond dark energy the universe contains on average zero or at most a single photon which if present immediately after turnaround has infinitesimally energy which subsequently blue shifts to produce $e^+e^-$ pairs. These statements are independent of the equation of state $\omega = p/\rho$ of dark energy provided $\omega < -1$. Thus $S_{cu} = 0$ and if observations confirm $\omega < -1$ the entropy problem is solved. We discuss the absence of a theoretical lower bound on $\phi = |\omega + 1|$, then describe an anthropic fine tuning argument that renders unlikely extremely small $\phi$. The present bound $\phi \lesssim 0.1$ already implies a time until turnaround of $(t_T - t_0) \gtrsim 100$ Gy.