Can dark matter–dark energy interaction alleviate the cosmic coincidence problem?

In this paper we study a model of interacting dark energy–dark matter where the ratio between these components is not constant, changing from early to late times in such a way that the model can solve or alleviate the cosmic coincidence problem (CP). The interaction arises from an assumed relation of the form ρx∝ρdα, where ρx and ρd are the energy densities of dark energy and dark matter components, respectively, and α is a free parameter. For a dark energy equation of state parameter w= - 1 we found that, if α= 0 , the standard Λ CDM model is recovered, where the coincidence problem is unsolved. For 0 < α< 1 , the CP would be alleviated and for α∼ 1 , the CP would be solved. The dark energy component is analyzed with both w= - 1 and w≠ - 1. Using Supernovae type Ia and Hubble parameter data constraints, in the case w= - 1 we find α=0.109-0.072+0.062 at 68% C.L., and the CP is alleviated. For w≠ - 1 , a degeneracy arises on the w–α plane. In order to break such degeneracy we add cosmic microwave background distance priors and baryonic acoustic oscillations data to the constraints, yielding α= - 0.075 ± 0.046 at 68% C.L. In this case we find that the CP is not alleviated even for 2σ interval for α. Furthermore, this last model is discarded against flat Λ CDM according to BIC analysis.