Probing the dark matter density evolution law with large scale structures

We propose a new method to explore a possible departure from the standard time evolution law for the dark matter density. We looked for a violation of this law by using a deformed evolution law, given by $\rho_c(z) \propto (1+z)^{3+\epsilon}$,andthenconstrain$\epsilon$. The dataset used for this purpose consists of Strong Gravitational Lensing data obtained from SLOAN Lens ACS, BOSS Emission-line Lens Survey, Strong Legacy Survey SL2S, and SLACS; along with galaxy cluster X-ray gas mass fraction measurements obtained using the Chandra Telescope. Our analyses show that $ϵ$ is consistent with zero within 1 $\sigma$ c.l., but the current dataset cannot rule out with high confidence level interacting models of dark matter and dark energy.