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

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