In this paper we present the equations of the evolution of the universe in $D$ spatial dimensions, as a generalization of the work of Lima citep{lima}. We discuss the Friedmann-Robertson-Walker cosmological equations in $D$ spatial dimensions for a simple fluid with equation of state $p=omega_{D}rho$. It is possible to reduce the multidimensional equations to the equation of a point particle system subject to a linear force. This force can be expressed as an oscillator equation, anti-oscillator or a free particle equation, depending on the $k$ parameter of the spatial curvature. An interesting result is the independence on the dimension $D$ in a de Sitter evolution. We also stress the generality of this procedure with a cosmological $Lambda$ term. A more interesting result is that the reduction of the dimensionality leads naturally to an accelerated expansion of the scale factor in the plane case.
We analyze the interaction between Dark Energy and Dark Matter from a thermodynamical perspective. By assuming they have different temperatures, we study the possibility of occurring a decay from Dark Matter into Dark Energy, characterized by a negative parameter $Q$. We find that, if at least one of the fluids has non vanishing chemical potential, for instance $mu_x<0$ and $mu_{dm}=0$ or $mu_x=0$ and $mu_{dm}>0$, the decay is possible, where $mu_x$ and $mu_{dm}$ are the chemical potentials of Dark Energy and Dark Matter, respectively. Using recent cosmological data, we find that, for a fairly simple interaction, the Dark Matter decay is favored with a probability of $sim 93%$ over the Dark Energy decay. This result comes from a likelihood analysis where only background evolution has been considered.
The thermodynamic properties of dark energy fluids described by an equation of state parameter $omega=p/rho$ are rediscussed in the context of FRW type geometries. Contrarily to previous claims, it is argued here that the phantom regime $omega<-1$ is not physically possible since that both the temperature and the entropy of every physical fluids must be always positive definite. This means that one cannot appeal to negative temperature in order to save the phantom dark energy hypothesis as has been recently done in the literature. Such a result remains true as long as the chemical potential is zero. However, if the phantom fluid is endowed with a non-null chemical potential, the phantom field hypothesis becomes thermodynamically consistent, that is, there are macroscopic equilibrium states with $T>0$ and $S>0$ in the course of the Universe expansion. Further, the negative value of the chemical potential resulting from the entropy constraint ($S>0$) suggests a bosonic massless nature to the phantom particles.
The accretion of a phantom fluid with non-zero chemical potential by black holes is discussed with basis on the Generalized Second Law of thermodynamics. For phantom fluids with positive temperature and negative chemical potential we demonstrate that the accretion process is possible, and that the condition guaranteeing the positiveness of the phantom fluid entropy coincides with the one required by Generalized Second Law. In particular, this result provides a complementary confirmation that cosmological phantom fluids do not need to have negative temperatures.
It is widely assumed that the observed universe is accelerating due to the existence of a new fluid component called dark energy. In this article, the thermodynamics consequences of a nonzero chemical potential on the dark energy component is discussed with special emphasis to the phantom fluid case. It is found that if the dark energy fluid is endowed with a negative chemical potential, the phantom field hypothesis becomes thermodynamically consistent with no need of negative temperatures as recently assumed in the literature.
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 ($omega lesssim -10/21$).
