Entropy of Contracting Universe in Cyclic Cosmology

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 $\varphi =|\omega +1|$, then describe an anthropic fine tuning argument that renders unlikely extremely small $\varphi$. The present bound $\varphi \lesssim 0.1$ already implies a time until turnaround of $(t_T-t_0)\gtrsim 100$ Gy.

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• Cosmic Evolution in a Cyclic Universe
• A Cyclic Model of the Universe
• Turnaround in Cyclic Cosmology
• Why the cosmological constant is small and positive
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