A low-$z$ test for interacting dark energy

A non-minimal coupling between the dark matter and dark energy components may offer a way of solving the so-called coincidence problem. In this paper we propose a low-$z$ test for such hypothesis using measurements of the gas mass fraction $f_{\mathrm{g}\mathrm{a}\mathrm{s}}$ in relaxed and massive galaxy clusters. The test applies to any model whose dilution of dark matter is modified with respect to the standard $a^{-3}$ scaling, as usual in interacting models, where $a$ is the cosmological scale factor. We apply the test to current $f_{\mathrm{g}\mathrm{a}\mathrm{s}}$ data and perform Monte Carlo simulations to forecast the necessary improvements in number and accuracy of upcoming observations to detect a possible interaction in the cosmological dark sector. Our results show that improvements in the present relative error ${\sigma }_{\mathrm{g}\mathrm{a}\mathrm{s}}\mathrm{/}{f}_{\mathrm{g}\mathrm{a}\mathrm{s}}$ are more effective to achieve this goal than an increase in the size of the $f_{\mathrm{g}\mathrm{a}\mathrm{s}}$ sample.