Violation of the equivalence principle in curvature-based extended gravity at finite temperature

Abstract

We review the possible violation of the Equivalence Principle at finite temperature [Formula: see text] in the framework of curvature-based Extended Theories of Gravity. Specifically, we first show how it is possible to derive Equivalence Principle violation from Quantum Field Theory at [Formula: see text]. Subsequently, we exhibit how this result can be precisely recovered by following an alternative path that envisages the employment of generalized Einstein equations with a temperature-dependent energy-momentum tensor. Finally, we adopt the latter formalism in the context of some Extended Gravity models to quantify the amount of Equivalence Principle violation. Specifically, Brans–Dicke Theory, Standard Model Extension and Conformal Gravity are considered in detail.