  We investigate the proof of concept and the implications of \textit{refracted
gravity}, a novel modified gravity aimed to solve the discrepancy between the
luminous and the dynamical mass of cosmic structures without resorting to dark
matter. Inspired by the behavior of electric fields in matter, refracted
gravity introduces a gravitational permittivity that depends on the local mass
density and modifies the standard Poisson equation. The resulting gravitational
field can become more intense than the Newtonian field and can mimic the
presence of dark matter. We show that the refracted gravitational field
correctly describes (1) the rotation curves and the Tully-Fisher relation of
disk galaxies; and (2) the observed temperature profile of the X-ray gas of
galaxy clusters. According to these promising results, we conclude that
refracted gravity deserves further investigation.
