Models of universe with a polytropic equation of state: II. The late universe

TL;DR

This paper develops models of the universe with a generalized polytropic equation of state, exploring late universe behavior, cyclic and eternal models, and connections between early and late cosmic phases, including scalar field potentials.

Contribution

It introduces new cosmological models with a generalized equation of state for negative polytropic indices, unifying early and late universe behaviors and addressing the cosmological constant problem.

Findings

Model of late universe with inflationary expansion and dark energy transition

Cyclic universe model with periodic appearance and disappearance

Eternal universe model without singularities and symmetry between early and late phases

Abstract

We construct models of universe with a generalized equation of state $p=(\alpha \rho+k\rho^{1+1/n})c^2$ having a linear component and a polytropic component. In this paper, we consider negative indices $n<0$. In that case, the polytropic component dominates in the late universe where the density is low. For $\alpha=0$, $n=-1$ and $k=-\rho_{\Lambda}$, we obtain a model of late universe describing the transition from the matter era to the dark energy era. The universe exists eternally in the future and undergoes an inflationary expansion with the cosmological density $\rho_{\Lambda}=7.02 10^{-24} g/m^3$ on a timescale $t_{\Lambda}=1.46 10^{18} s$. For $\alpha=0$, $n=-1$ and $k=\rho_{\Lambda}$, we obtain a model of cyclic universe appearing and disappearing periodically. If we were living in this universe, it would disappear in about 2.38 billion years. We make the connection between the early and the late universe and propose a simple equation describing the whole evolution of the universe. This leads to a model of universe that is eternal in past and future without singularity (aioniotic universe). This model exhibits a nice "symmetry" between an early and late phase of inflation, the cosmological constant in the late universe playing the same role as the Planck constant in the early universe. The Planck density and the cosmological density represent fundamental upper and lower bounds differing by 122 orders of magnitude. The cosmological constant "problem" may be a false problem. We determine the potential of the scalar field (quintessence, tachyon field) corresponding to the generalized equation of state $p=(\alpha \rho+k\rho^{1+1/n})c^2$. We also propose a unification of pre-radiation, radiation and dark energy through the quadratic equation of state $p/c^2=-4\rho^2/3\rho_P+\rho/3-4\rho_{\Lambda}/3$.