An estimate of the dark matter density from galaxy clusters and supernovae data

In this paper, we discuss a model-independent way to obtain the present dark matter density parameter ($Omega_{rm{c,0}}$) by combining gas mass fraction measurements in galaxy clusters ($f_{gas}$), type Ia supernovae (SNe Ia) observations and measurements of the cosmic baryon abundance from observations of absorption systems at high redshifts. Our estimate is $Omega_{rm{c,0}} = 0.244 pm 0.013$ ($1sigma$). By considering the latest local measurement of the Hubble constant, we obtain $Omega_{rm{M,0}} = 0.285 pm 0.013$ ($1sigma$) for the total matter density parameter. We also investigate departures of the evolution of the dark matter density with respect to the usual $a^{-3}$ scaling, as usual in interacting models of dark matter and dark energy. As the current data cannot confirm or rule out such an interaction, we perform a forecast analysis to estimate the necessary improvements in number and accuracy of upcoming $f_{gas}$ and SNe Ia observations to detect a possible non-minimal coupling in the cosmological dark sector.