  If visible matter alone is present in the Universe, general relativity (GR)
and its Newtonian weak field limit (WFL) cannot explain several pieces of
evidence, from the largest to the smallest scales. The most investigated
solution is the cosmological model $\Lambda$ cold dark matter ($\Lambda$CDM),
where GR is valid and two dark components are introduced, dark energy (DE) and
dark matter (DM), to explain the $\sim$70\% and $\sim$25\% of the mass-energy
budget of the Universe, respectively. An alternative approach is provided by
modified gravity theories, where a departure of the gravity law from
$\Lambda$CDM is assumed, and no dark components are included. This work
presents refracted gravity (RG), a modified theory of gravity formulated in a
classical way where the presence of DM is mimicked by a gravitational
permittivity $\epsilon(\rho)$ monotonically increasing with the local mass
density $\rho$, which causes the field lines to be refracted in small density
environments. Specifically, the flatter the system the stronger the refraction
effect and thus, the larger the mass discrepancy if interpreted in Newtonian
gravity. RG presented several encouraging results in modelling the dynamics of
disk and elliptical galaxies and the temperature profiles of the hot X-ray
emitting gas in galaxy clusters and a covariant extension of the theory seems
to be promising.
