Chemical Potential and the Nature of the Dark Energy: The case of phantom

TL;DR

This paper explores how a non-zero chemical potential influences dark energy's properties, revealing that its sign and magnitude constrain the equation of state parameter and the nature of dark energy, including phantom and vacuum states.

Contribution

It introduces a thermodynamic framework incorporating chemical potential into dark energy models, analyzing its effects on the equation of state and particle spectra for bosons and fermions.

Findings

Positive chemical potential restricts ; negative allows phantom behavior.

Dark energy with ; fermions with ; bosons with .

Thermodynamics constrains ; results close to acceleration threshold.

Abstract

The influence of a possible non zero chemical potential $\mu$ on the nature of dark energy is investigated by assuming that the dark energy is a relativistic perfect simple fluid obeying the equation of state (EoS), $p=\omega \rho$ ($\omega <0, constant$). The entropy condition, $S \geq 0$, implies that the possible values of $\omega$ are heavily dependent on the magnitude, as well as on the sign of the chemical potential. For $\mu >0$, the $\omega$-parameter must be greater than -1 (vacuum is forbidden) while for $\mu < 0$ not only the vacuum but even a phantomlike behavior ($\omega <-1$) is allowed. In any case, the ratio between the chemical potential and temperature remains constant, that is, $\mu/T=\mu_0/T_0$. Assuming that the dark energy constituents have either a bosonic or fermionic nature, the general form of the spectrum is also proposed. For bosons $\mu$ is always negative and the extended Wien's law allows only a dark component with $\omega < -1/2$ which includes vacuum and the phantomlike cases. The same happens in the fermionic branch for $\mu <0$. However, fermionic particles with $\mu >0$ are permmited only if $-1 < \omega < -1/2$. The thermodynamics and statistical arguments constrain the EoS parameter to be $\omega < -1/2$, a result surprisingly close to the maximal value required to accelerate a FRW type universe dominated by matter and dark energy ($\omega \lesssim -10/21$).