Growth of structures and redshift-space distortion data in scale-dependent gravity

This study is devoted to the implications of scale-dependent gravity in Cosmology. Redshift-space distortion data indicate that there is a tension between Λ CDM and available observations as far as the value of the rms density fluctuation, σ₈, is concerned. It has been pointed out that this tension may be alleviated in alternative theories in which gravity is weaker at redshift z∼ 1. We study the evolution of density perturbations for non-relativistic matter on top of a spatially flat FLRW Universe, and we compute the combination A= fσ₈ in the framework of scale-dependent gravity, where both Newton’s constant and the cosmological constant are allowed to vary with time. Upon comparison between available observational data (supernovae data as well as redshift-space distortion data) and theoretical predictions of the model, we determine the numerical value of σ₈ that best fits the data.