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

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, $S\ge 0$, 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 ($\omega \lesssim -10/21$).

7 pages, 5 figures

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• Thermodynamics of a transient phantom scenario
• A Thermodynamic Model for Dark Energy Including Particle Creation or Destruction Processes