Multimetric extension of the PPN formalism: experimental consistency of repulsive gravity

TL;DR

This paper extends the PPN formalism to multimetric gravity theories with dark sectors, tests their experimental consistency in the solar system, and refines the theory to align with observations while maintaining cosmological benefits.

Contribution

It develops a multimetric PPN formalism, applies it to a dark matter model, and improves the theory for experimental consistency without losing cosmological advantages.

Findings

Initial theory inconsistent with solar system tests

Simplified PPN formalism enables parameter calculation

Refined theory aligns with experimental data

Abstract

Recently we discussed a multimetric gravity theory containing several copies of standard model matter each of which couples to its own metric tensor. This construction contained dark matter sectors interacting repulsively with the visible matter sector, and was shown to lead to cosmological late-time acceleration. In order to test the theory with high-precision experiments within the solar system we here construct a simple extension of the parametrized post-Newtonian (PPN) formalism for multimetric gravitational backgrounds. We show that a simplified version of this extended formalism allows the computation of a subset of the PPN parameters from the linearized field equations. Applying the simplified formalism we find that the PPN parameters of our theory do not agree with the observed values, but we are able to improve the theory so that it becomes consistent with experiments of post-Newtonian gravity and still features its promising cosmological properties.