Probing interaction in the dark sector

A phenomenological attempt at alleviating the so-called coincidence problem is to allow the dark matter and dark energy to interact. By assuming a coupled quintessence scenario characterized by an interaction parameter $ϵ$, we investigate the precision in the measurements of the expansion rate $H(z)$ required by future experiments in order to detect a possible deviation from the standard $\mathrm{\Lambda }$CDM model ($ϵ=0$). We perform our analyses at two levels, namely: through Monte Carlo simulations based on $ϵ$CDM models, in which $H(z)$ samples with different accuracies are generated and through an analytic method that calculates the error propagation of $ϵ$ as a function of the error in $H(z)$. We show that our analytical approach traces simulations accurately and find that to detect an interaction {using $H(z)$ data only, these must reach an accuracy better than 1%.