Cosmological perturbations in mimetic gravity models

The so-called LambdaCDM model of cosmology has been very successful at explaining all cosmological observations. Various attempts are ongoing in explaining the effect of a cosmological constant Lambda in terms of a modification of gravity w.r.t to Einstein General Relativity. Recently, an interesting scenario has been proposed, the so called mimetic gravity. In this scenario the dark matter components of the universe (dark matter and dark energy contributions) can be mimicked purely with a modification of gravity. In general this is achieved starting from a given initial theory and applying to it a non-invertible disformal transformation (the original paper by Chamsedinne and Mukhanov started from the Einstein-Hilbert action to provide a new theory where a new degree of freedom could mimick a cold dark matter componentâ ''mimetic dark matter''). The status of these scenarios is mature enough to study their cosmological perturbations with the goal of extracting some obervational predictions of particular interest for forthcoming Large Scale Structure surveys, like the one the forthcoming Euclid satellite mission will provide. The goal of this thesis is to make a detailed computation of the observational predictions for mimetic gravity models.