Extended EPS structure for $f(R, R_{\mu\nu} R^{\mu\nu})$ gravity theories in Palatini formalism

Details

Written by Azam Izadi

An axiomatic understanding of the foundations of any reasonable theory of the space--time and gravity was represented by Ehlers, Pirani and Schild (EPS), which leaves a special effect on the observational protocols in such a way that not all standard protocols can be trivially extended to a general extended theory of gravity. In addition, for a generic Palatini modified gravity theory, in a frame with the locally vanishing affine connection, the degeneracy of known aspects of the speed of light is breaking in the presence of matter and hence results in breaking the equivalence principle. Furthermore, some aspects of it may become variable in the aforementioned local frame. Following these results, we consider a general $f(R, R_{\mu\nu} R^{\mu\nu})$ gravity theory in the Palatini formalism. We study the equivalence principle and different manifestations of the speed of light in this general theory. In addition, the EPS structure on the space-time is extended for this generic Palatini gravity theories. Finally, we compare the results with standard GR.