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

TL;DR

This paper develops a phenomenological cyclic universe model with periodic scale factors, analyzing acceleration-deceleration transitions, and fitting Hubble data to determine the universe's evolution and curvature dynamics.

Contribution

It introduces two models of cyclic universe expansion, with Model A fitting Hubble data and detailing the evolution of dark energy, dark matter, and curvature without standard inflation.

Findings

Initial acceleration transitions to deceleration at 3.313x10^{-38}s

Universe transitions from deceleration to acceleration at 6.713 Gyr

Final deceleration occurs at 38.140 Gyr, completing a 121.172 Gyr cycle

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.