Entropy of Contracting Universe in Cyclic Cosmology

Following up a recent proposal [1] for a cyclic model based on phantom dark energy, we examine the content of the contracting universe (cu) and its entropy Scu. 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 ω = p/ρ of dark energy provided ω < −1. Thus Scu = 0 and if observations confirm ω < −1 the entropy problem is solved. We discuss the absence of a theoretical lower bound on φ = |ω + 1|, then describe an anthropic fine tuning argument that renders unlikely extremely small φ. The present bound φ∼ 0.1 already implies a time until turnaround of (tT − t0) > ∼ 100 Gy. In a recent paper [1] we suggested a cyclic model which solves the entropy problem [2]. Technical calculations are certainly desirable to demonstrate the consistency of our model but we know of no fatal flaw. The most important new ingredient is the idea that the contracting universe has essentially zero entropy and comes back empty of matter. Here we take the model seriously #1 and examine more critically some general features including its possibilty of being tested. The contracting universe of the cyclic model contains dark energy with zero entropy and possibly, as was only generally stated in [1], a small amount of radiation which could possess entropy. The deflation at turnaround reduces entropy from a gigantic value O(> 10) to an extremely low value there cited as O(10). An unrealistic value for the dark energy equation of state ω = p/ρ = −4/3 was employed simply for algebraic simplicity as it makes ρΛ ∝ a, and no attempt was made at a realistic description of our universe. In the present article, we shall study the entropy of the contracting universe in this speculative scenario more quantitatively and now will use arbitrary ω = −1 − φ with φ > 0 so that ρΛ ∝ a . The quantity φ is the most important parameter for observational discrimination between this cyclic model and a cosmological constant . The next test of φ 6= 0 will likely come from the Planck Surveyor satellite [7]. One wonders, therefore, how different from zero φ is? There is no lower bound on φ to make the model work except that it must be non zero. We already know φ∼ 0.1 from the WMAP3 data [8]. If φ is truly infinitesimal, the test must await improved technology. To restore optimism we shall, at the end of the Letter, describe an anthropic fine tuning argument that shows that extremely small φ is unlikely. In [1], it was emphasized that the universe comes back empty of matter including black holes. The presence of matter during contraction causes apparently insuperable problems because accelerated structure formation will precipitate a premature bounce. Black holes, if present, will expand and proliferate with the same consequence. But the presence of radiation must also be carefully studied because although at turnaround the photon energy is infinitesimal (Eγ < ∼ 10 eV ), the blue shifting during contraction leads before the bounce to production of ee pairs, undesirable because generically they will create problems with continued contraction. As we shall show herein there are fortunately no photons in the contracting phase of the cycle, only the truly innocuous dark energy. The cyclic model contains one free parameter, the common density ρC at which the universe both turns around and bounces. Since the bounce is independent of ω we begin with it and take as bounce temperatures TB = 10 p GeV with, to be above the weak and below the Planck scales, 3 ≤ p ≤ 17. Using the derivation in [1] this gives ρC = ηρH2O where η = 10 and ρH20 = 1g/cm 3 is the density of water, an easily imaginable It has been said the problem is not that theoretical physicists take their own model too seriously but that they do not take it seriously enough [3]. and from the Steinhardt-Turok cyclic model [4–6].