# Equivalence principle violation at finite temperature in scalar-tensor gravity

## TL;DR

This paper investigates potential violations of the Equivalence Principle at finite temperature in scalar-tensor gravity, using quantum field theory and alternative approaches, with applications to specific metrics and constraints on Brans-Dicke theory.

## Contribution

It introduces a novel analysis of Equivalence Principle violation at finite temperature within scalar-tensor gravity using quantum field theory and alternative methods, applying it to specific models and constraining theory parameters.

## Key findings

- Equivalence Principle violation can occur at finite temperature in scalar-tensor gravity.
- The formalism applies to both generic diagonal metrics and Brans-Dicke theory.
- Experimental bounds can constrain parameters of scalar-tensor theories.

## Abstract

We analyze possible violations of the Equivalence Principle in scalar-tensor gravity at finite temperature $T.$ Before we present an approach where the Equivalence Principle violation is achieved within the framework of Quantum Field Theory. After, we rely on an alternative approach first proposed by Gasperini, which leads to the same outcome obtained in the framework of Quantum Field Theory (one-loop corrections) at finite $T$. Finally, we exhibit the application of the above formalism both to a generic diagonal metric, cast in spherical coordinates, and to the Brans-Dicke theory. In the last case, we show that it is possible to put a significant constraint on the free parameter of the theory by means of experimental bounds on the Equivalence Principle.