# Sub-subleading Soft Graviton Theorem in Generic Theories of Quantum Gravity

## TL;DR

This paper derives the sub-subleading soft graviton theorem for generic quantum gravity theories, providing a universal formula applicable to tree and loop amplitudes in higher dimensions, consistent with known results.

## Contribution

It presents a universal expression for sub-subleading soft graviton theorems applicable to generic theories of quantum gravity, valid in all dimensions at tree level and in higher dimensions at loop level.

## Key findings

- Universal soft graviton theorem derived for all space-time dimensions at tree level.
- Loop amplitude results valid in five or more dimensions due to infrared divergences.
- Consistency with existing quantum field theory and string theory results.

## Abstract

We analyze scattering amplitudes with one soft external graviton and arbitrary number of other finite energy external states carrying arbitrary mass and spin to sub-subleading order in the momentum of the soft graviton. Our result can be expressed as the sum of a universal part that depends only on the amplitude without the soft graviton and not the other details of the theory and a non-universal part that depends on the amplitude without the soft graviton, and the two and three point functions of the theory. For tree amplitudes our results are valid in all space-time dimensions while for loop amplitudes, infrared divergences force us to restrict our analysis to space time dimensions five or more. With this restriction the results are valid to all orders in perturbation theory. Our results agree with known results in quantum field theories and string theory.