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Equivalence between generalized phenomenological schemes for the interaction of cosmological fluids: applications to arbitrary linear barotropic fluids and vacuum decay

Interactions between cosmic fluids may appear in many cosmological scenarios that go far beyond the usually studied energy exchange in the dark sector. In the absence of known microscopic interaction mechanisms, phenomenological ansatzes are usually proposed in order to describe such models. In this paper, we derive a generalization of one of the most frequently used of such ansatzes:the one based on a initial proposal of Shapiro, Solà, España-Bonet and Ruiz-Lapuente who described a time-dependent cosmological "constant" whose variation arises from quantum effects near the Planck scale [I. L. Shapiro, J. Solà, C. España-Bonet, and P. Ruiz-Lapuente, (2003). This physically motivated model was based on a single free parameter $ν$, and was subsequently studied by Wang and Meng (2005), under the pure phenomenological reasoning that the vacuum decay would slightly modify the exponent describing how the energy density of dark matter decreases with the scale factor. This modification is described by a single parameter $\varepsilon$ (= 3 $ν$ of the former paper). The generalization derived in the present article requires two free parameters ($\varepsilon_{1}$, $\varepsilon_{2}$). We show that this extension is dynamically equivalent to the ansatz proposed by Barrow and Clifton (2006) which deals with the transfer of energy between any two fluids using a two-parameter scheme ($α_{1}$, $α_{2}$) and that has the advantage of exhibiting explicitly the form of the interaction factor appearing in the continuity equation of each fluid.