On a class of scaling FRW cosmological models

Abstract

We study Friedmann-Robertson-Walker cosmological models with mattercontent composed of two perfect fluids ρ1 and ρ2, withbarotropic pressure densities p1/ρ1 = ω1 = const and p2/ρ2 = ω2 = const, where one of the energy densities is givenby ρ1 = C1aα+C2aβ, with C1, C2, αand β taking constant values. We solve the field equations byusing the conservation equation without breaking it into twointeracting parts with the help of a coupling interacting term Q.Nevertheless, with the found solution may be associated aninteracting term Q, and then a number of cosmological interactingmodels studied in the literature correspond to particular cases ofour cosmological model. Specifically those models having constantcoupling parameters α̃, β̃ andinteracting terms given by Q = α̃HρDM,Q = α̃HρDE, Q = α̃H(ρDM+ρDE) and Q = α̃HρDM+β̃HρDE, where ρDM andρDE are the energy densities of dark matter and darkenergy respectively. The studied set of solutions contains a classof cosmological models presenting a scaling behavior at early and atlate times. On the other hand the two-fluid cosmological modelsconsidered in this paper also permit a three fluid interpretationwhich is also discussed. In this reinterpretation, for flatFriedmann-Robertson-Walker cosmologies, the requirement ofpositivity of energy densities of the dark matter and dark energycomponents allows the state parameter of dark energy to be in therange −1.37≲ωDE < −1/3.