Late universe dynamics with scale-independent linear couplings in the dark sector

We explore the dynamics of cosmological models with two coupled dark components with energy densities rho(A) and rho(B) and constant equation of state (EOS) parameters w(A) and w(B). We assume that the coupling is of the form Q = Hq(rho(A,) rho(B)), so that the dynamics of the two components turns out to be scale independent, i.e. does not depend explicitly on the Hubble scalar H. With this assumption, we focus on the general linear coupling q = q(o) + q(A)rho(A) + q(B)rho(B), which may be seen as arising from any q(rho(A), rho(B)) at late time and leads in general to an effective cosmological constant. In the second part of the paper we consider observational constraints on the form of the coupling from SN Ia data, assuming that one of the components is cold dark matter (CDM), i.e. w(B) = 0, while for the other the EOS parameter can either have a standard (w(A) > -1) or phantom (w(A) < -1) value. We find that the constant part of the coupling function is unconstrained by SN Ia data and, among typical linear coupling functions, the one proportional to the dark energy density rho(A) is preferred in the strong coupling regime, vertical bar q(A)vertical bar > 1. Models with phantom w(A) favor a positive coupling function, increasing rho(A). In models with standard w(A), not only a negative coupling function is allowed, transferring energy to CDM, but the uncoupled subcase falls at the border of the likelihood.