Inflation's gravitational wave fingerprint fades exponentially at high frequencies

Primordial gravitational waves from inflation naively grow without bound at small scales — a physically meaningless result that requires careful regularization. This work shows that the smoother the transition between inflation and the hot Big Bang, the more sharply that power drops at high frequencies, with infinitely smooth transitions producing a clean exponential cutoff. If such a cutoff is ever detected, its shape and location would directly reveal when and at what energy inflation ended.