Interaction in the dark sector: a phenomenological approach

The non-gravitational interaction between the dark components of the Universe could lead to the variation of dark matter energy density standard evolution law. When we assume this scenario, the dark matter energy density follows $\rho_{{dm}}\sim(1+z)^{3 + \epsilon(z)}$ (where $\epsilon(z)=0$ the standard law is recovered). In this paper, we perform a Bayesian analysis to test three parameterizations for $\epsilon(z)$, namely: $\epsilon(z)=\epsilon_0$, $\epsilon(z)=\epsilon_0 + \epsilon_1\frac{z}{1+z}$ and $\epsilon(z)=\epsilon_0 + \epsilon_1\frac{z(1+z)}{1+z^2}$, where the first one is motivated through the fundamental grounds and the others are on the phenomenological ones. Through the Gaussian process regression, our method uses galaxy cluster gas mass fraction measurements, SNe Ia observations, Cosmic Chronometers, and BAO data. No specific cosmological model is considered. In all possibilities analyzed, the standard evolution law ($\epsilon(z)=0$) is within $2\sigma$ c.l. The investigated cases generally indicated scenarios of inconclusive or weak evidence toward the simplest model from the Bayesian standpoint.