Soft Gravitons, Hard Truths: Infrared Safety of Particle Processes in a Gravitational-Wave Background

Gravitational waves are thought to propagate unattenuated through matter due to a cancellation between graviton absorption and stimulated emission inferred from leading-order soft-graviton arguments. We revisit this reasoning and show that it fails for the converse problem: the effect of a gravitational-wave background on matter. For unstable particles, real graviton emission \emph{and} absorption appear to enhance decay rates. By extending the soft-graviton framework describing real and virtual processes in a gravitational wave background, and resumming them to all orders, we show that inclusive decay rates remain essentially unchanged. The mutual transparency between matter and gravitational radiation thus follows from infrared safety, and not from a fortuitous cancellation in the lowest-order approximation of exclusive rates.