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

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 Wiens 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 ($omega lesssim -10/21$).