f(R) Gravitation Theories

The f(R) theories gained interest since the 1980s when it was proposed to model the inflation scenarios with higher order Ricci scalar functions, so that singularities were avoided. It sought to preserve the same principles with which General Relativity was formulated: the principle of strong equivalence, the movement of particles following space-time geodesics and without adding extra fields, which is why they are considered “pure” metric theories. The formal context is based on the article by Thomas P. Sotiriou and Valerio Faraoni, f(R) theories of gravity. Note here that Einstein’s equation is shared by two models. On the other hand, the action can be varied in two different ways, depending on the dependence of the variables.