A Cosmological Model Describing the Early Inflation, the Intermediate Decelerating Expansion, and the Late Accelerating Expansion of the Universe by a Quadratic Equation of State

Abstract

Universe 2015, xx 2 infinite past). On the other hand, it admits a scalar field interpretation based on an inflaton, quintessence, or tachyonic field. Our model generalizes the standard ΛCDM model by incorporating naturally a phase of early inflation that avoids the primordial singularity. Furthermore, it describes the early inflation, the intermediate decelerating expansion, and the late accelerating expansion of the universe simultaneously in terms of a single equation of state. We determine the corresponding scalar field potential that unifies the inflaton and quintessence potentials.

On a quadratic equation of state and a universe mildly bouncing above the Planck temperature

“…where t cb is another integration constant. This scale factor agrees with the one obtained by Chavanis in appendix A of his second paper in reference [7]. Figure 1 shows this scale factor together with the one of the ΛCDM universe,…”

Friedmann-Lemaitre cosmologies via roulettes and other analytic methods

“…We may compare our results with the α-fluid model studied in [24] for which the equation of state is…”

Observational constraints on the extended Chaplygin gas inflation

“…Now, we believed that the universe expands with acceleration (Kaiser 2014) and there are several models to describe such expansion. One of them is a barotropic matter with an equation of state p = ωρ (Peebles and Ratra 2003), while there are some models with quadratic equation of state (Ananda and Bruni 2006;Chavanis 2013;Linder and Scherrer 2009),…”