# Hidden Simplicity of the Gravity Action

## TL;DR

This paper introduces a simplified representation of the Einstein-Hilbert action, recasting it as a cubic theory that streamlines graviton perturbation calculations and enables new recursion relations for scattering amplitudes.

## Contribution

It presents a novel cubic formulation of the Einstein-Hilbert action that simplifies graviton perturbation theory and scattering amplitude computations.

## Key findings

- Derived new cubic form of Einstein-Hilbert action
- Established off-shell recursion relations for graviton scattering
- Constructed a compact gauge-fixed form of the action

## Abstract

We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons and a single auxiliary field. The corresponding equations of motion are the Einstein field equations rewritten as two coupled first-order differential equations. Since all Feynman diagrams are cubic, we are able to derive new off-shell recursion relations for tree-level graviton scattering amplitudes. With a judicious choice of gauge fixing, we then construct an especially compact form for the Einstein-Hilbert action in which all graviton interactions are simply proportional to the graviton kinetic term. Our results apply to graviton perturbations about an arbitrary curved background spacetime.