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Register a new userWeak Lensing of the CMB: Sampling Errors on B-Modes
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Kendrick M. Smith
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The B modes generated by the lensing of CMB polarization are a primary target for the upcoming generation of experiments and can potentially constrain quantities such as the neutrino mass and dark energy equation of state. The net sample variance on the small scale B modes out to l=2000 exceeds Gaussian expectations by a factor of 10 reflecting the variance of the larger scale lenses that generate them. It manifests itself as highly correlated band powers with correlation coefficients approaching 70% for wide bands of Delta l/l ~0.25. It will double the total variance for experiments that achieve a sensitivity of approximately 4 uK-arcmin and a beam of several arcminutes or better. This non-Gaussianity must be taken into account in the analysis of experiments that go beyond first detection.
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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.
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Detailed measurements of the CMB lensing signal are an important scientific goal of ongoing ground-based CMB polarization experiments, which are mapping the CMB at high resolution over small patches of the sky. In this work we simulate CMB polarization lensing reconstruction for the $EE$ and $EB$ quadratic estimators with current-generation noise levels and resolution, and show that without boundary effects the known and expected zeroth and first order $N^{(0)}$ and $N^{(1)}$ biases provide an adequate model for non-signal contributions to the lensing power spectrum estimators. Small sky areas present a number of additional challenges for polarization lensing reconstruction, including leakage of $E$ modes into $B$ modes. We show how simple windowed estimators using filtered pure-$B$ modes can greatly reduce the mask-induced mean-field lensing signal and reduce variance in the estimators. This provides a simple method (used with recent observations) that gives an alternative to more optimal but expensive inverse-variance filtering.
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