# One-loop corrections to infrared GWs is forbidden by symmetries

## TL;DR

This paper proves that one-loop quantum corrections to large-scale primordial gravitational waves are forbidden by symmetries, resolving a long-standing controversy in inflationary cosmology.

## Contribution

It provides a symmetry-based proof, using Ward identities, that one-loop corrections to large-scale tensor perturbations vanish, confirming previous results for scalar perturbations.

## Key findings

- One-loop corrections cancel on large scales.
- Symmetry arguments prevent one-loop corrections.
- Results are consistent with previous scalar perturbation studies.

## Abstract

Small-scale scalar perturbations amplified during inflation can induce primordial gravitational waves through tensor-scalar interactions. A long-standing controversial issue is whether the one-loop corrections to tensor perturbations exist on large scales. Firstly, we demonstrate through direct one-loop calculations that one-loop corrections cancel each other out on large scales. We then proceed from the symmetry of the interacting system and directly prove, based on the Ward identity, the absence of one-loop corrections on large scales-without the need for specific loop diagram calculations. This is consistent with the results we previously obtained for scalar perturbations.