Gravitational lensing on the Cosmic Microwave Background by gravity waves

We study the effect of a stochastic background of gravitational waves on the gravitational lensing of the Cosmic Microwave Background (CMB) radiation. It has been shown that matter density inhomogeneities produce a smoothing of the acoustic peaks in the angular power spectrum of the CMB anisotropies. A gravitational wave background gives rise to an additional smoothing of the spectrum. For the most simple case of a gravitational wave background arising during a period of inflation, the effect results to be three to four orders of magnitude smaller than its scalar counterpart, and is thus undetectable. It could play a more relevant role in models where a larger background of gravitational waves is produced.