Observational constraints on the product of dark energy chemical potential and number density in out-of-equilibrium models

TL;DR

This paper constrains the product of dark energy chemical potential and number density using observational data and thermodynamic principles in out-of-equilibrium models, revealing a preference for negative chemical potential and phantom behavior.

Contribution

It introduces combined thermodynamic and observational constraints on dark energy out-of-equilibrium models, providing bounds on chemical potential and particle creation/destruction rates.

Findings

Dark energy chemical potential must be negative.

Thermodynamic bounds depend on particle creation or destruction.

Small negative alpha values are compatible with observational data.

Abstract

In this work, we impose observational limits on the product of dark energy chemical potential, $\mu$, and number density, $n$, at the present time in out-of-equilibrium models, considering that particles can be created or destroyed in the fluid at a rate $\Gamma=3\alpha H(a)$, where $\alpha$ is a constant and $H(a)\equiv\dot{a}/a$ is the Hubble parameter. We combine the bounds derived from the positivity of entropy and the second law of thermodynamics with observational constraints on the Chevallier-Polarski-Linder (CPL) and Barboza-Alcaniz (BA) parameterizations of the equation of state (EoS) of the component. We use Type Ia supernovae (SN Ia) data from Pantheon+; baryon acoustic oscillation (BAO) data from DESI DR2; and cosmic microwave background (CMB) measurements from Planck. For $\alpha>0$ (particle creation), the thermodynamic restrictions yield only upper limits for the $\mu_{0}n_{0}$ product, while in the case of $\alpha<0$ (particle destruction) they establish both upper and lower limits, allowing for a range of values to be obtained. In both scenarios, however, we find that the chemical potential of dark energy must be negative, $\mu<0$, which indicates a preference for the phantom regime. In particular, when $\alpha<0$, it is noted that the thermodynamic bounds are simultaneously compatible only for very small absolute values of $\alpha$, with $\alpha=-0.0002$ being the limiting case and resulting in $\mu_{0}n_{0}(\alpha=-0.0002)=-2.2_{-0.7}^{+1.0}\,\,GeV/m^{3}$.