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Cosmic microwave background (CMB) experiments, which currently provide some of the most powerful cosmological data sets, will become much more constraining in the near future. While these measurements promise to teach us more about the nature of dark energy, inflation and neutrino physics, increased precision will require special attention dedicated to the data analysis. In this talk I will focus on the gravitational lensing of the CMB and some of its implications. By introducing a novel analysis technique, applying it to the Planck satellite data and commenting on improvements which will be possible with a CMB Stage 4 experiment, I will first show how we can utilize CMB gravitational lensing to probe self-consistency of the CMB data sets. Then I will overview how gravitational lensing induces non-Gaussian covariances between the CMB data and how these covariances affect constraints on the cosmological parameters.

The observables of the large-scale structure such as galaxy number density generally depends on the density environment (of a few hundred Mpc). The dependence can traditionally be studied by performing gigantic cosmological N-body simulations and measuring the observables in different density environments. Alternatively, we perform the so-called "separate universe simulations", in which the effect of the environment is absorbed into the change of the cosmological parameters. For example, an overdense region is equivalent to a universe with positive curvature, hence the structure formation changes accordingly compared to the region without overdensity. In this talk, I will introduce the "separate universe mapping", and present how the power spectrum
and halo mass function change in different density environments, which are equivalent to the squeezed bispectrum and the halo bias, respectively. I will then discuss the extension of this approach to inclusion of additional fluids such as massive neutrinos. This allows us to probe the novel scale-dependence of halo bias and squeezed bispectrum caused by different evolutions of the background overdensities of cold dark matter and the additional fluid. Finally, I will present one application of the separate universe simulations to predict the squeezed bispectrum formed by small-scale Lyman-alpha forest power spectrum and large-scale lensing convergence, and compare with the measurement from BOSS Lyman-alpha forest and Planck lensing map.

The standard structure formation model is based on the Cold Dark Matter (CDM) hypothesis where non-gravitational dark matter interactions are irrelevant for the formation and evolution of galaxies. Surprisingly, current observations allow for significant departures from the CDM hypothesis,

which could potentially leave signatures of the dark matter particle nature in the properties of galaxies. In this talk, I will describe a framework we have proposed that generalizes the theory of structure formation (in both the linear and non-linear regimes) to include new dark matter physics in order to explore galaxy formation and evolution in the broadest sense.