The dark matter problem from f(R) gravity viewpoint

Abstract An alternative view to the dark matter puzzle is represented by Extended Theories of Gravity. The approach consists in addressing issues like dark components from the point of view of gravitational field instead of requiring new material ingredients that, up to now, have not been detected at fundamental level. In this review paper, by extending the Hilbert‐Einstein action of gravitational field to more general actions (e.g. f(R) gravity), it is shown that several gravitating structures like stars, spiral galaxies, elliptical galaxies and clusters of galaxies can be self‐consistently described without asking for dark matter. It is also shown that standard General Relativity tests and Equivalence Principle constraints can be evaded at Solar System scales.