Cosmic acceleration from a single fluid description

TL;DR

This paper introduces a novel equation of state inspired by solid state physics to explain cosmic acceleration without dark energy, fitting cosmological data and extending logotropic models.

Contribution

It proposes the Anton-Schmidt equation of state for matter, linking solid state properties to cosmological acceleration, and demonstrates its consistency with observational data.

Findings

The model can reproduce cosmic acceleration without dark energy.

Constraints on parameters n and B are consistent with observations.

The approach includes ΛCDM as a limiting case.

Abstract

We here propose a new class of barotropic factor for matter, motivated by properties of isotropic deformations of crystalline solids. Our approach is dubbed Anton-Schmidt's equation of state and provides a non-vanishing, albeit small, pressure term for matter. The corresponding pressure is thus proportional to the logarithm of universe's volume, i.e. to the density itself since $V\propto \rho^{-1}$. In the context of solid state physics, we demonstrate that by only invoking standard matter with such a property, we are able to frame the universe speed up in a suitable way, without invoking a dark energy term by hand. Our model extends a recent class of dark energy paradigms named \emph{logotropic} dark fluids and depends upon two free parameters, namely $n$ and $B$. Within the Debye approximation, we find that $n$ and $B$ are related to the Gr\"uneisen parameter and the bulk modulus of crystals. We thus show the main differences between our model and the logotropic scenario, and we highlight the most relevant properties of our new equation of state on the background cosmology. Discussions on both kinematics and dynamics of our new model have been presented. We demonstrate that the $\Lambda$CDM model is inside our approach, as limiting case. Comparisons with CPL parametrization have been also reported in the text. Finally, a Monte Carlo analysis on the most recent low-redshift cosmological data allowed us to place constraints on $n$ and $B$. In particular, we found $n=-0.147^{+0.113}_{-0.107}$ and $B=3.54 \times 10^{-3}$.