Is Lensing Amplitude Anomaly in the Cosmic Microwave Background the Evidence of Extremely Low Frequency Primordial Gravitational Wave?

Abstract: 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.