Precision cosmology with CMB lensing, delensing and cross-correlation with galaxy surveys

The upcoming generation of CMB polarization experiments (Simons Observatory, CMB-S4) and large-scale structures (LSS) surveys (Euclid, LSST) will map the matter distribution of the universe using the weak gravitational lensing effect. Being able to model this effect with the required level of precision will be mandatory in order to exploit these observables and their cross-correlations for cosmological applications. After reviewing the status of CMB and galaxy surveys cross-correlation, I will discuss recent developments in the theoretical modeling of CMB lensing and its cross-correlation with LSS probes including the non-linear evolution of the matter distribution and consequences of multiple deflections of photons. In the second part of the talk I will present the recent results of POLARBEAR, one of the current ongoing CMB polarization experiments. I will focus in particular on its recent analysis that achieved the first delensing of B-modes of CMB polarization using CMB data alone, paving the way for the optimal analysis of B-modes experiments of the next decade that will improve our knowledge of inflation by more than an order of magnitude.