Non-Parametric Analysis for the Dark Matter Density Evolution

In this paper, we investigate a potential departure in the standard dark matter density evolution law, ${\rho }_{dm}={\rho }_{dm,0}(1+z{)}^3$. The method involves considering a deformed evolution model, denoted as ${\rho }_{dm}={\rho }_{dm,0}(1+z{)}^{3}f(z)$, and searching the presence of any deviation ($f(z)\mathrm{\ne }1$). As one may see, $f(z)$ is a general function that parametrizes a possible digression from the standard law. We use data of baryon acoustic oscillations, type I Supernovae luminosity distances, and galaxy cluster gas mass fraction observations to reconstruct $f(z)$ through an approach that is not dependent on the cosmological model or the so-called Gaussian process regression. Unlike previous works, it enables us to investigate a possible deviation without using a specific function to describe it. We have obtained $f(z)=1$, the standard model scenario, within $2\sigma$ c.l. in all the considered cases.