f(R) Theories Of Gravity

Modified gravity theories have received increased attention lately due to combined motivation coming from high-energy physics, cosmology and astrophysics. Among numerous alternatives to Einstein’s theory of gravity, theories which include higher order curvature invariants, and specifically the particular class of f® theories, have a long history. In the last five years there has been a new stimulus for their study, leading to a number of interesting results. We review here f® theories of gravity in an attempt to comprehensively present their most important aspects and cover the largest possible portion of the relevant literature. All known formalisms are presented – metric, Palatini and metric-affine – and the following topics are discussed: motivation; actions, field equations and theoretical aspects; equivalence with other theories; cosmological aspects and constraints; viability criteria; astrophysical applications.