An equivalence principle for scalar forces

TL;DR

This paper examines the conditions under which a scalar field can satisfy an equivalence principle similar to gravity, analyzing the effects of scalar-matter coupling and interactions on the principle's validity.

Contribution

It clarifies the status of the scalar equivalence principle, showing its stability under renormalizations and identifying conditions for its violation.

Findings

Scalar-matter coupling can be stable against renormalizations.

Equivalence principle holds unless scalar or graviton self-interactions are significant.

Black holes violate the scalar equivalence principle due to graviton self-interactions.

Abstract

The equivalence of inertial and gravitational masses is a defining feature of general relativity. Here, we clarify the status of the equivalence principle for interactions mediated by a universally coupled scalar, motivated partly by recent attempts to modify gravity at cosmological distances. Although a universal scalar-matter coupling is not mandatory, once postulated, it is stable against classical and quantum renormalizations in the matter sector. The coupling strength itself is subject to renormalization of course. The scalar equivalence principle is violated only for objects for which either the graviton self-interaction or the scalar self-interaction is important---the first applies to black holes, while the second type of violation is avoided if the scalar is Galilean-symmetric.