Constraining stochastic gravitational wave background from weak lensing of CMB B-modes

TL;DR

This paper investigates how a stochastic gravitational wave background influences CMB B-modes through weak lensing, deriving constraints on its energy density without assuming specific models, and highlighting the importance of polarization rotation effects.

Contribution

It introduces a method to constrain the SGWB's spectral energy density from CMB weak lensing effects, emphasizing the role of polarization rotation alongside deflection.

Findings

Derived bounds on $oldsymbol{ ext{Ω}_{GW}}$ for various models.

Identified the threshold for observable imprints in CMB B-modes.

Quantified the relative importance of deflection and rotation effects.

Abstract

A stochastic gravitational wave background (SGWB) will affect the CMB anisotropies via weak lensing. Unlike weak lensing due to large scale structure which only deflects photon trajectories, a SGWB has an additional effect of rotating the polarization vector along the trajectory. We study the relative importance of these two effects, deflection \& rotation, specifically in the context of E-mode to B-mode power transfer caused by weak lensing due to SGWB. Using weak lensing distortion of the CMB as a probe, we derive constraints on the spectral energy density ($\Omega_{GW}$) of the SGWB, sourced at different redshifts, without assuming any particular model for its origin. We present these bounds on $\Omega_{GW}$ for different power-law models characterizing the SGWB, indicating the threshold above which observable imprints of SGWB must be present in CMB.