Serial Acceleration-Deceleration Transitions in a Cyclic Universe with Negative Curvature

Abstract

In this work we develop a general phenomenological model of the Cyclic Universe. We construct periodic scale factor a(t) from the requirements of the periodicity of a(t) with no singular behavior at the turning points t_\alpha and t_\omega and the requirement that a unique analytical form of the Hubble function H(z) can be derived from the Hubble function H(t) to fit the data on H(z). We obtain two versions of a(t) called Model A and Model C. Hubble data select Model A. With the analytical forms of the Hubble functions H(t) and H(z) known we calculate the deceleration parameters q(t) and q(z) to study the acceleration-deceleration transitions during the expansion phase. We find that the initial acceleration at t_\alpha=0 transits at t_{ad1}=3.313x10^{-38}s into deceleration period that transits at t_{da}=6.713 Gyr to the present period of acceleration. The present acceleration shall end in a transition to the final deceleration at t_{ad2}=38.140 Gyr. The expansion period lasts 60.586 Gyr. The complete cycle period is T=121.172 Gyr. We use the deceleration parameters q(z) and q(t) to solve the Friedmann equations for the energy densities of Dark Energy \Omega_0 and Dark Matter \Omega_M to describe their evolutions over a large range of z and t. We show that in the Model A the curvature density \Omega_c(z) evolves from a flat Universe in the early times to a curves anti de-Sitter spacetime today. There is no Standard Model Inflation in the Model A.