On a class of scaling FRW cosmological models

Abstract

We study Friedmann-Robertson-Walker cosmological models with matter content composed of two perfect fluids $\rho_1$ and $\rho_2$, with barotropic pressure densities $p_1/ \rho_1=\omega_1=const$ and $p_2/ \rho_2=\omega_2=const$, where one of the energy densities is given by $\rho_1=C_1 a^\alpha + C_2 a^\beta$, with $C_1$, $C_2$, $\alpha$ and $\beta$ 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 parameters $\tilde{\alpha}$, $\tilde{\beta}$ and interacting terms given by $Q=\tilde{\alpha} H \rho_{_{DM}}$, $Q=\tilde{\alpha} H \rho_{_{DE}}$, $Q=\tilde{\alpha} H (\rho_{_{DM}}+ \rho_{_{DE}})$ and $Q=\tilde{\alpha} H \rho_{_{DM}}+\tilde{\beta} H \rho_{_{DE}}$, where $\rho_{_{DM}}$ and $\rho_{_{DE}}$ 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 $-1.37 \lesssim \omega_{_{DE}}<-1/3$.