Chemical potential and the nature of dark energy: The case of a phantom field

The influence of a possible nonzero chemical potential μ 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, p=ωρ (ω<0, constant). The entropy condition, S≥0, implies that the possible values of ω are heavily dependent on the magnitude, as well as on the sign of the chemical potential. For μ>0, the ω parameter must be greater than -1 (vacuum is forbidden) while for μ<0 not only the vacuum but even a phantomlike behavior (ω<-1) is allowed. In any case, the ratio between the chemical potential and temperature remains constant, that is, μ/T=μ₀/T₀. Assuming that the dark energy constituents have either a bosonic or fermionic nature, the general form of the spectrum is also proposed. For bosons μ is always negative and the extended Wien's law allows only a dark component with ω<-1/2, which includes vacuum and the phantomlike cases. The same happens in the fermionic branch for μ<0. However, fermionic particles with μ>0 are permitted only if -1<ω<-1/2. The thermodynamics and statistical arguments constrain the equation-of-state parameter to be ω<-1/2, a result surprisingly close to the maximal value required to accelerate a Friedmann-Robertson-Walker--type universe dominated by matter and dark energy (ω-10/21).