The Parameterised Post-Newtonian Limit of Bimetric Theories of Gravity

TL;DR

This paper analyzes the post-Newtonian limit of general bimetric gravity theories, showing they can closely mimic general relativity in solar system tests and exploring the behavior of massive modes and parameter discontinuities.

Contribution

It extends the parameterized post-Newtonian framework to bimetric theories, identifying new potentials and analyzing the effects of massive modes on gravitational predictions.

Findings

Bimetric theories can evade solar system tests with sufficiently large masses.

No van Dam-Veltman-Zakharov discontinuity in gamma parameter in the massless limit.

Discontinuities in other post-Newtonian parameters occur as massive modes become massless.

Abstract

We consider the post-Newtonian limit of a general class of bimetric theories of gravity, in which both metrics are dynamical. The established parameterised post-Newtonian approach is followed as closely as possible, although new potentials are found that do not exist within the standard frame-work. It is found that these theories can evade solar system tests of post-Newtonian gravity remarkably well. We show that perturbations about Minkowski space in these theories contain both massless and massive degrees of freedom, and that in general there are two different types of massive mode, each with a different mass parameter. If both of these masses are sufficiently large then the predictions of the most general class of theories we consider are indistinguishable from those of general relativity, up to post-Newtonian order in a weak field, low velocity expansion. In the limit that the massive modes become massless, we find that these general theories do not exhibit a van Dam-Veltman-Zakharov-like discontinuity in their gamma parameter, although there are discontinuities in other post-Newtonian parameters as the massless limit is approached. This smooth behaviour in gamma is due to the discontinuities from each of the two different massive modes cancelling each other out. Such cancellations cannot occur in special cases with only one massive mode, such as the Isham-Salam-Strathdee theory.