One-loop corrections to infrared GWs is forbidden by symmetries

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.