# On the uniqueness of ghost-free special gravity

## TL;DR

This paper characterizes the most general ghost-free special gravity theories with abelian gauge invariance, aiding the understanding of gravity's uniqueness and exploring gauge-invariant matter couplings.

## Contribution

It determines the broadest class of ghost-free special gravity theories with second-order equations of motion and discusses gauge-invariant matter couplings.

## Key findings

- Identified the general form of ghost-free special gravity theories.
- Established conditions for second-order equations of motion.
- Explored gauge-invariant couplings to matter fields.

## Abstract

Special gravity refers to interacting theories of massless gravitons in Minkowski space-time which are invariant under the abelian gauge invariance $h_{ab}\rightarrow h_{ab}+\partial_{(a}\chi_{b)}$ only. In this article we determine the most general form of special gravity free of Ostrogradski ghosts, meaning its equation of motion is of at most second order. Together with the recent works, this result could be helpful in formulating proofs of General Relativity as the unique physical theory of self-interacting massless gravitons. We also study how to construct gauge invariant couplings to matter fields.