Una formulazione covariante alla Gravità Rifratta

We propose a covariant version of $\textit{Refracted Gravity}$ (RG), a novel modified theory of gravity that attempts to describe the dynamics of cosmic structures without resorting to the existence of dark matter. \\ $\textit{Refracted Gravity}$ was originally proposed as a phenomenological model where the modified Poisson equation contains a monotonic function of the local mass density, the gravitational permittivity, that boosts the gravitational field in low-density environments. \\ We show that the covariant version of $\textit{Refracted Gravity}$ belongs to the larger family of the Scalar-Tensor theories of gravitation and thus shares most of their general features. Specifically, we show how the gravitational permittivity can be associated with an extra scalar field, beyond the gravitational field. As a first application of this approach, we compute a vacuum Schwarzschild-like solution. \\ On the cosmological framework, we compute a modified version of the Friedmann equations, proposing a generalization of the cosmological constant, in terms of a function of the dynamic scalar field. This quantity, thus, unlike in General Relativity, evolves with time and suggests that the scalar field is also responsible for the accelerated expansion of the Universe. \\ $\textit{Refracted Gravity}$, in its relativistic extension, proposes the existence of a possible intriguing link between phenomena currently separately attributed to dark matter and dark energy.\\ Furthermore, we compute the effective equation of state of dark energy in this framework, showing that covariant $\textit{Refracted Gravity}$ predicts a varying parameter $w_{DE}$ with redshift, which approaches the present value of $-1$, in agreement with current observational constraints.\\ Finally, we start investigating the application of linear cosmological perturbation theory to RG.