A comparison of CMB lensing efficiency of gravitational waves and large
  scale structure
  We provide a detailed treatment and comparison of the weak lensing effects
due to large-scale structure (LSS), or scalar density perturbations and those
due to gravitational waves(GW) or tensor perturbations, on the temperature and
polarization power spectra of the Cosmic Microwave Background (CMB). We carry
out the analysis both in real space by using the correlation function method,
as well as in the spherical harmonic space. We find an intriguing similarity
between the lensing kernels associated with LSS lensing and GW lensing. It is
found that the lensing kernels only differ in relative negative signs and their
form is very reminiscent of even and odd parity bipolar spherical harmonic
coefficients. Through a numerical study of these lensing kernels, we establish
that lensing due to GW is more efficient at distorting the CMB spectra as
compared to LSS lensing, particularly for the polarization power spectra.
Finally we argue that the CMB B-mode power spectra measurements can be used to
place interesting constraints on GW energy densities.
