# Diagrammar in an Extended Theory of Gravity

## TL;DR

This paper demonstrates how to construct the $S$-matrix for an extended gravity theory using factorisation, showing it retains the same soft singularity properties as Einstein gravity, including sub-sub-leading terms.

## Contribution

It introduces a method to derive the $S$-matrix of an extended gravity theory from three-point amplitudes, preserving key soft theorems.

## Key findings

- $S$-matrix constructed from three-point amplitudes obeys soft theorems
- Tree amplitudes exhibit the same soft singularities as Einstein gravity
- Sub-sub-leading soft terms are preserved in the extended theory

## Abstract

We show how the $S$-matrix of an extended theory of gravity defined by its three-point amplitudes can be constructed by demanding factorisation. The resultant $S$-matrix has tree amplitudes obeying the same soft singularity theorems as Einstein gravity including the sub-sub-leading terms.