Testing generalized logotropic models with cosmic growth

TL;DR

This paper evaluates four logotropic dark energy models against observational data, finding that some variants are statistically comparable or slightly favored over the standard DM model, but all face perturbation stability issues.

Contribution

It introduces and tests a generalized logotropic model with a split between dark matter and baryons, comparing its performance to other logotropic and DM models using observational data.

Findings

The Anton-Schmidt model with rac{5}{6} is ruled out.

The generalized logotropic fluid is most suitable but weakly disfavored.

The DM model remains statistically superior.

Abstract

We check the dynamical and observational features of four typologies of logotropic dark energy models, leading to a \emph{thermodynamic cosmic speed up} fueled by a single fluid that unifies dark energy and dark matter. We first present two principal Anton-Schmidt fluids where the Gr\"uneisen parameter $\gamma_{\rm G}$ is free to vary and then fixed to the special value $\gamma_{\rm G}=\tfrac{5}{6}$. We also investigate the pure logotropic model, corresponding to $\gamma_{\rm G}=-\frac{1}{6}$. Finally, we propose a new logotropic paradigm that works as a generalized logotropic fluid, in which we split the role of dark matter and baryons. We demonstrate that the logotropic paradigms may present drawbacks in perturbations, showing a negative adiabatic sound speed which make perturbations unstable. The Anton-Schmidt model with $\gamma_{\rm G}=\frac{5}{6}$ is ruled out while the generalized logotropic fluid seems to be the most suitable one, albeit weakly disfavored than the $\Lambda$CDM model. We combine low- and higher-redshift domains through experimental fits based on Monte Carlo Markov Chain procedures, taking into account supernovae Ia catalogue, Hubble measurements and $\sigma_8$ data points. We consider two model selection criteria to infer the statistical significance of the four models. We conclude there is statistical advantage to handle the Anton-Schmidt fluid with the Gr\"uneisen parameter free to vary and/or fixed to $\gamma_{\rm G}=-\frac{1}{6}$. The generalized logotropic fluid indicates suitable results, statistically favored than the other models, until the sound speed is positive, becoming unstable in perturbations elsewhere. We emphasize that the $\Lambda$CDM paradigm works statistically better than any kinds of logotropic and generalized logotropic models, while the Chevallier-Polarski-Linder parametrization is statistically comparable with logotropic scenarios.