CMB Lensing: Polarization, Large-Scale Structure and the Primordial Bispectrum

Gravitational lensing of photons in the Cosmic Microwave Background (CMB) can be described by an integrated potential along the line of sight, the CMB lensing potential. Covariances in maps of the CMB are generated by the lensing effect, and are used to reconstruct the lensing potential itself, which is a useful probe of the matter distribution. The CMB lensing potential has been measured to high significance with CMB temperature data. However, signal to noise for lensing reconstruction from CMB polarization data is expected to be much better due to the presence of the lensing B-mode. Upcoming data from ground based CMB polarization instruments will provide high resolution maps over small patches of the sky. This will provide much better lensing reconstruction, but also presents data analysis challenges. This thesis begins with an introduction to the field of CMB lensing and CMB lensing reconstruction. The second chapter details the biases present in reconstructing the lensing potential from CMB polarization maps considering first the full sky, and then small patches of sky. It also shows that using the pure-B mode formalism for the CMB polarization leads to improved lensing reconstruction over the naive case on the cut sky. Given the upcoming improvement in the CMB lensing reconstruction, it is expected that cross-correlations of the CMB lensing with other structure tracers, such as galaxies, will yield improved information for cosmology. It is also expected that the CMB lensing will become useful to help constrain uncertainties in the galaxy power spectrum, and provide information on the linear galaxy bias and redshift distribution. The third chapter of the thesis forecasts the power of cross correlation science for a number of galactic and non-galactic parameters. Finally, the CMB lensing effects the level of non-Gaussianity observed in the CMB. The fourth chapter of the thesis is a study of the lensing effect on the primordial squeezed bispectrum. We conclude in the fifth chapter.