Exploring the expansion of the universe using the Gr\"uneisen parameter

TL;DR

This paper links the universe's expansion to the Gr"uneisen parameter from condensed matter physics, suggesting a phase transition and time-dependent dark energy effects, providing a novel interdisciplinary perspective.

Contribution

It introduces the effective Gr"uneisen parameter as a tool to analyze cosmological expansion and connects it with the Einstein field equations, revealing new insights into dark energy and phase transitions.

Findings

Dark energy implies a metastable state with negative pressure.

The effective Gr"uneisen parameter is embedded in Einstein's equations.

A phase transition-like behavior occurs during the shift from decelerated to accelerated expansion.

Abstract

For a perfect fluid, pressure $p$ and energy density $\rho$ are related via the equation of state (EOS) $\omega = p/\rho$, where $\omega$ is the EOS parameter, being its interpretation usually constrained to a numerical value for each universe era. Here, based on the Mie-Gr\"uneisen EOS, we show that $\omega$ is recognized as the effective Gr\"uneisen parameter $\Gamma_{eff}$, whose singular contribution, the so-called Gr\"uneisen ratio $\Gamma$, quantifies the barocaloric effect. Our analysis suggests that the negative $p$ associated with dark-energy implies a metastable state and that in the dark-energy-dominated era $\omega$ is time-dependent, which reinforces recent proposals of a time-dependent cosmological constant. Furthermore, we demonstrate that $\Gamma_{eff}$ is embodied in the energy-momentum stress tensor in the Einstein field equations, enabling us to analyse, in the frame of an imperfect fluid picture, anisotropic effects of the universe expansion. We propose that upon going from decelerated- to accelerated-expansion, a phase transition-like behavior can be inferred. Yet, our analysis in terms of entropy, $\Gamma$, and a by us adapted version of Avramov/Casalini's model to Cosmology unveil hidden aspects related to the expansion of the universe. Our findings pave the way to interpret cosmological phenomena in connection with concepts of condensed matter Physics via $\Gamma_{eff}$.