Quantum Equivalence Principle Violations in Scalar-Tensor Theories

TL;DR

This paper investigates quantum effects in scalar-tensor theories, revealing that while classical symmetries uphold the weak equivalence principle, quantum corrections induce small violations and alter the action's structure.

Contribution

It demonstrates how Ward identities from broken Weyl symmetry predict quantum-induced violations of the weak equivalence principle in scalar-tensor theories.

Findings

Ward identities ensure weak equivalence principle at all orders in classical theory

Quantum corrections lead to suppressed violations of the equivalence principle

Matter couplings to scalar fields cause deviations from classical predictions

Abstract

We study the equivalence principle and its violations by quantum effects in scalar-tensor theories that admit a conformal frame in which matter only couples to the spacetime metric. These theories possess Ward identities that guarantee the validity of the weak equivalence principle to all orders in the matter coupling constants. These Ward identities originate from a broken Weyl symmetry under which the scalar field transforms by a shift, and from the symmetry required to couple a massless spin two particle to matter (diffeomorphism invariance). But the same identities also predict violations of the weak equivalence principle relatively suppressed by at least two powers of the gravitational couplings, and imply that quantum corrections do not preserve the structure of the action of these theories. We illustrate our analysis with a set of specific examples for spin zero and spin half matter fields that show why matter couplings do respect the equivalence principle, and how the couplings to the gravitational scalar lead to the weak equivalence principle violations predicted by the Ward identities.