# On gravitational wave modes in Nash theory of gravity

## TL;DR

This paper investigates gravitational wave modes in Nash gravity, revealing standard and massive graviton solutions, and introduces a modified version to align with general relativity in the weak field limit.

## Contribution

It analyzes gravitational wave modes in Nash gravity and proposes a modified version that reproduces GR behavior in the weak field regime.

## Key findings

- Standard wave equation solutions match general relativity
- Discovery of massless and massive graviton modes
- Constraints on graviton mass parameter

## Abstract

In this Letter, we consider original Nash theory of gravity. In terms of the scalar fields representation, Nash gravity is equivalent to the action of bi-scalar tensor gravity with four derivative terms of metric tensor. We then quantify the ghost in the theory. In order to study the gravitational wave modes of the theory, we perform a small perturbation over a fixed Minkowski background. We discover the standard wave equation and obtain the solutions as those of the standard general relativity. In order to satisfy the GR in the weak field limit, we further modify the original Nash theory by adding the Einstein-Hibert term called modified Nash gravity. In this theory, we once study the gravitational wave modes. We derive equations of motion and examine the solutions. We discover the two-mode solutions: the massless graviton and the massive one. Using a uniform prior probability on the graviton mass, we can constrain mass parameter.