No-go theorem for bimetric gravity with positive and negative mass

TL;DR

This paper proves a no-go theorem showing that all bimetric gravity theories predicting opposite forces on positive and negative masses in the Newtonian limit are impossible, challenging models explaining dark matter via negative mass.

Contribution

It establishes a general no-go theorem for bimetric gravity theories with opposite forces on positive and negative masses in the Newtonian limit.

Findings

No bimetric gravity models with opposite Newtonian forces on positive and negative masses exist.

The theorem applies to the most general linearized bimetric theories compatible with physical assumptions.

Results challenge the negative mass explanation for dark matter in bimetric gravity.

Abstract

We argue that the most conservative geometric extension of Einstein gravity describing both positive and negative mass sources and observers is bimetric gravity and contains two copies of standard model matter which interact only gravitationally. Matter fields related to one of the metrics then appear dark from the point of view of an observer defined by the other metric, and so may provide a potential explanation for the dark universe. In this framework we consider the most general form of linearized field equations compatible with physically and mathematically well-motivated assumptions. Using gauge-invariant linear perturbation theory, we prove a no-go theorem ruling out all bimetric gravity theories that, in the Newtonian limit, lead to precisely opposite forces on positive and negative test masses.