Cosmological Inference Beyond the Two-Point Correlation Functions

The two-point statistics such as the matter power spectrum or the cosmic microwave background (CMB) temperature spectrum in cosmology contain essential information of the universe. This thesis presents an investigation of the physics beyond the standard two-point statistics in both galaxy and CMB surveys. We point out the time delay effect in CMB lensing is not negligible – the last scattering surface is not a perfect sphere, and construct an approach of measuring the distortions in the observed CMB fields. The signal-to-noise ratio of the map is detectable for the dipole moment therefore providing possibilities of observing this effect on the largest scales in future surveys. Next we look into large scale matter density modes which are difficult to be measured directly due to observational systematic effects. We study the approach of measuring the linear density modes by indirectly observing their impact on small scale perturbations. Physically speaking small scale structure will grow faster in a more dense area due to a stronger gravitational potential. We also generalize this method to include galaxy bias, redshift space distortion and light-cone effects to prepare for potential applications in spectroscopic surveys. Finally we establish a deep neural network based on the super resolution technique to reconstruct CMB convergence field using observed polarizations. Next generation CMB surveys are designed to have unprecedented low level of noise, thus the main challenge in the traditional appoaches of CMB lensing reconstruction would be recapturing small scale features. Our generative adversarial network (GAN) targets at reconstructing high resolution maps. We also compare the result with a previous deep learning approach – ResidualUNet.