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 $rho_B$. 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 $q=q_o+q_Arho_A+q_Brho_B$, 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. 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, $|q_{A}|>1$. While phantom models favor a positive coupling function, in non-phantom models, not only a negative coupling function is allowed, but the uncoupled sub-case falls at the border of the likelihood.