On a class of scaling FRW cosmological models

Abstract

We study Friedmann-Robertson-Walker cosmological models with matter content composed of two perfect fluids ρ1 and ρ2, with barotropic pressure densities p1/ρ1 = ω1 = const and p2/ρ2 = ω2 = const, where one of the energy densities is given by ρ1 = C1a α + C2a β , with C1, C2, α and β taking constant values. We solve the field equations by using the conservation equation without breaking it into two interacting parts with the help of a coupling interacting term Q. Nevertheless, with the found solution may be associated an interacting term Q, and then a number of cosmological interacting models studied in the literature correspond to particular cases of our cosmological model. Specifically those models having constant coupling parametersα,β and interacting terms given by Q =αHρ DM , Q =αHρ DE , Q =αH(ρ DM + ρ DE ) and Q =αHρ DM +βHρ DE , where ρ DM and ρ DE are the energy densities of dark matter and dark energy respectively. The studied set of solutions contains a class of cosmological models presenting a scaling behavior at early and at late times. On the other hand the two-fluid cosmological models considered in this paper also permit a three fluid interpretation which is also discussed. In this reinterpretation, for flat Friedmann-Robertson-Walker cosmologies, the requirement of positivity of energy densities of the dark matter and dark energy components allows the state parameter of dark energy to be in the range −1.37 ω DE < −1/3.

Thermodynamics of interacting holographic dark energy

“…Several model have been considered in the literature where Q is a function of the energy densities and the Hubble parameter [36], considering that equations ( 4) and ( 5) can be integrated straightforwardly [37]. In the present study, we do not assume this coupling term a priori, but rather study the system through the field equations and remain as general as possible as done by [38,13]. We consider the coincidence parameter r(a) as an auxiliary variable, defined as the ratio between the two energy densities…”