  Trajectories of photons of cosmic microwave background (CMB) from the surface
of last scattering to us could be deflected by extremely low frequency
primordial gravitational wave (PGW). With large scale structure (LSS) producing
a smoothing of the acoustic peaks in the power spectrum of the CMB anisotropies
through weak lensing, the presence of extremely low frequency PGW could enhance
the effect of weak lensing on CMB due to the coupling of extremely low
frequency PGW and LSS, thus, give rise to much more smoothing of the spectrum.
This may be an natural explanation for the lensing amplitude anomaly observed
by Planck, meaning that lensing amplitude anomaly may be the evidence of
extremely low frequency PGW.
