Generalized Logotropic Models and their Cosmological Constraints

TL;DR

This paper introduces a new class of cosmological models called Generalized Logotropic Models, which unify dark matter and dark energy through a single fluid with a parameter n, and analyzes their evolution and singularity behaviors.

Contribution

It proposes a generalized framework extending the original logotropic model with a free parameter n, exploring its cosmological implications and asymptotic behaviors.

Findings

Favored low n values (≤3) for realistic models.

Identified conditions leading to little rip and big rip scenarios.

Predicted big rip timing as a function of n without free parameters.

Abstract

We propose a new class of cosmological unified dark sector models called "{\em Generalized Logotropic Models}". They depend on a free parameter $n$. The original logotropic model [P.H. Chavanis, Eur. Phys. J. Plus {\bf 130}, 130 (2015)] is a special case of our generalized model corresponding to $n=1$. In our scenario, the Universe is filled with a single fluid, a generalized logotropic dark fluid (GLDF), whose pressure $P$ includes higher order logarithmic terms of the rest-mass density $\rho_m$. The total energy density $\epsilon$ is the sum of the rest-mass energy density $\rho_m c^2$ and the internal energy density $u$ which play the role of dark matter energy density $\epsilon_m$ and dark energy density $\epsilon_{de}$, respectively. We investigate the cosmological behavior of the generalized logotropic models by focusing on the evolution of the energy density, scale factor, equation of state parameter, decceleration parameter and squared speed of sound. Low values of $n\le 3$ are favored. We also study the asymptotic behavior of the generalized logotropic models. In particular, we show that the model presents a phantom behavior and has three distinct ways of evolution depending on the value of $n$. For $n\le 2$, it leads to a little rip and for $n>2$ to a big rip. We predict the value of the big rip time as a function of $n$ without any free (undetermined) parameter.