Inferring S_8(z) and gamma (z) with cosmic growth rate measurements using machine learning

Abstract

Measurements of the cosmological parameter S_8 provided by cosmic microwave background and large scale structure data reveal some tension between them, suggesting that the clustering features of matter in these early and late cosmological tracers could be different. In this work, we use a supervised learning method designed to solve Bayesian approach to regression, known as Gaussian Processes regression, to quantify the cosmic evolution of S_8 up to z sim 1.5. For this, we propose a novel approach to find firstly the evolution of the function sigma _8(z), then we find the function S_8(z). As a sub-product we obtain a minimal cosmological model-dependent sigma _8(z=0) and S_8(z=0) estimates. We select independent data measurements of the growth rate f(z) and of [fsigma _8](z) according to criteria of non-correlated data, then we perform the Gaussian reconstruction of these data sets to obtain the cosmic evolution of sigma _8(z), S_8(z), and the growth index gamma (z). Our statistical analyses show that S_8(z) is compatible with Planck Lambda CDM cosmology; when evaluated at the present time we find sigma _8(z=0) = 0.766 pm 0.116 and S_8(z=0) = 0.732 pm 0.115. Applying our methodology to the growth index, we find gamma (z=0) = 0.465 pm 0.140. Moreover, we compare our results with others recently obtained in the literature. In none of these functions, i.e. sigma _8(z), S_8(z), and gamma (z), do we find significant deviations from the standard cosmology predictions.