# Post-Newtonian parameter $\gamma$ and the deflection of light in ghost-free massive bimetric gravity

## TL;DR

This paper investigates the PPN parameter gamma in ghost-free massive bimetric gravity, deriving constraints from solar system light deflection measurements and discussing implications for dark matter and galactic mergers.

## Contribution

It provides the first calculation of the PPN gamma parameter in ghost-free massive bimetric gravity and compares it with observational data to constrain the theory's parameters.

## Key findings

- PPN gamma parameter derived for spherically symmetric systems
- Bounds on theory parameters from solar system light deflection
- Agreement with galaxy-scale light deflection observations

## Abstract

We consider the parametrized post-Newtonian (PPN) limit of ghost-free massive bimetric gravity with two mutually non-interacting matter sectors coupled to the two metrics. Making use of a gauge-invariant differential decomposition of the metric perturbations, we solve the field equations up to the linear PPN order for a static, point-like mass source. From the result we derive the PPN parameter $\gamma$ for spherically symmetric systems, which describes the gravitational deflection of light by visible matter. By a comparison to its value measured in the solar system we obtain bounds on the parameters of the theory. We further discuss the deflection of light by dark matter and find an agreement with the observed light deflection by galaxies. We finally speculate about a possible explanation for the observed distribution of dark matter in galactic mergers such as Abell 520 and Abell 3827.