Motion of a "small body" in non-metric gravity

TL;DR

This paper investigates the motion of small bodies within a non-metric gravity framework, revealing they follow geodesics of a specially constructed metric and establishing a standard matter coupling scheme.

Contribution

It introduces a modified gravity theory based on a potential added to Plebanski formulation, maintaining degrees of freedom and defining matter coupling in a standard metric background.

Findings

Small bodies move along geodesics of a new metric.

The theory retains the same degrees of freedom as GR.

A prescription for matter coupling in the modified theory is provided.

Abstract

We describe "small bodies" in a non-metric gravity theory previously studied by this author. The main dynamical field of the theory is a certain triple of two-forms rather than the metric, with only the spacetime conformal structure, not metric, being canonically defined. The theory is obtained from general relativity (GR) in Plebanski formulation by adding to the action a certain potential. Importantly, the modification does not change the number of propagating degrees of freedom as compared to GR. We find that "small bodies" move along geodesics of a certain metric that is constructed with the help of a new potential function that appears in the matter sector. We then use the "small body" results to formulate a prescription for coupling the theory to general stress-energy tensor. In its final formulation the theory takes an entirely standard form, with matter propagating in a metric background and only the matter-gravity coupling and the gravitational dynamics being modified. This completes the construction of the theory and opens way to an analysis of its physical predictions.