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

Abstract

AbstractIn 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 $$\rho _x\propto \rho _d^\alpha $$ ρ x ∝ ρ d α , where $$\rho _x$$ ρ x and $$\rho _d$$ ρ d are the energy densities of dark energy and dark matter components, respectively, and $$\alpha $$ α is a free parameter. For a dark energy equation of state parameter $$w=-1$$ w = - 1 we found that, if $$\alpha =0$$ α = 0 , the standard $$\Lambda $$ Λ CDM model is recovered, where the coincidence problem is unsolved. For $$0<\alpha <1$$ 0 < α < 1 , the CP would be alleviated and for $$\alpha \sim 1$$ α ∼ 1 , the CP would be solved. The dark energy component is analyzed with both $$w=-1$$ w = - 1 and $$w\ne -1$$ w ≠ - 1 . Using Supernovae type Ia and Hubble parameter data constraints, in the case $$w=-1$$ w = - 1 we find $$\alpha =0.109^{+0.062}_{-0.072}$$ α = 0 . 109 - 0.072 + 0.062 at 68% C.L., and the CP is alleviated. For $$w\ne -1$$ w ≠ - 1 , a degeneracy arises on the w–$$\alpha $$ α plane. In order to break such degeneracy we add cosmic microwave background distance priors and baryonic acoustic oscillations data to the constraints, yielding $$\alpha =-0.075\pm 0.046$$ α = - 0.075 ± 0.046 at 68% C.L.. In this case we find that the CP is not alleviated even for 2$$\sigma $$ σ interval for $$\alpha $$ α . Furthermore, this last model is discarded against flat $$\Lambda $$ Λ CDM according to BIC analysis.