Chemical Potential and the Nature of the Dark Energy: The case of phantom - AstrophysicsReport as inadecuate

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Abstract: The influence of a possible non zero chemical potential $\mu$ on the natureof dark energy is investigated by assuming that the dark energy is arelativistic perfect simple fluid obeying the equation of state EoS,$p=\omega ho$ $\omega <0, constant$. The entropy condition, $S \geq 0$,implies that the possible values of $\omega$ are heavily dependent on themagnitude, 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 $\omega <-1$ isallowed. In any case, the ratio between the chemical potential and temperatureremains constant, that is, $\mu-T=\mu 0-T 0$. Assuming that the dark energyconstituents have either a bosonic or fermionic nature, the general form of thespectrum is also proposed. For bosons $\mu$ is always negative and the extendedWien-s law allows only a dark component with $\omega < -1-2$ which includesvacuum 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 theEoS parameter to be $\omega < -1-2$, a result surprisingly close to the maximalvalue required to accelerate a FRW type universe dominated by matter and darkenergy $\omega \lesssim -10-21$.

Author: J. A. S. Lima, S. H. Pereira


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