Testing generalized logotropic models with cosmic growth

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 Grüneisen parameter ${\gamma }_{\mathrm{G}}$ is free to vary and then fixed to the special value ${\gamma }_{\mathrm{G}}=\frac{5}{6}$. We also investigate the pure logotropic model, corresponding to ${\gamma }_{\mathrm{G}}=-\frac{1}{6}$. 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 ${\gamma }_{\mathrm{G}}=\frac{5}{6}$ 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 Grüneisen parameter free to vary and/or fixed to ${\gamma }_{\mathrm{G}}=-\frac{1}{6}$. 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.

arXiv comment15 pages, 3 tables, 4 figures. It matches the published version

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