Modulations of the CMB

Cosmic microwave background (CMB) anisotropies are Gaussian and isotropic at linear order. The presence of long wavelength modulating fields, however, can introduce non-Gaussianity and statistical anisotropy in the CMB. There are discrepancies between the observed CMB lensing signal and theoretical expectations. We explore the possibility that compensated isocurvature perturbations or spatial fluctuations in the fine-structure constant could solve this problem. The imprint of both these possibilities on CMB statistics is computed. Current data are used to probe these models, forecasts are made for the sensitivity of upcoming efforts like CMB Stage IV , and a variety of other theoretical considerations are explored.