The physics and statistics of nonlinear gravitational clustering

The study of nonlinear gravitational effect on large scale structure has great implications on cosmology. It is essential to understand how nonlinear gravity affects cosmological signals in this era of precision cosmology. I demonstrate how approximate collapse models can be used to describe the nonlinear gravitational effect. In particular, I show how the ellipsoidal collapse model can be thought of as improving both the spherical model and the Zeldovich approximation. This greatly simplifies the use of the ellipsoidal collapse model in other studies of structure formation. Its applications in the calculation of nonlinear probability distribution function (PDF) in real and redshift space show excellent agreement with numerical measurements. A related study demonstrates a reconstruction method of the initial fluctuation field from the evolved measurements. This reconstruction works great for real and redshift space measurements and provides the first step to methods that improve the gravitational smeared BAO signals.;The effect of primordial non-Gaussianity on large scale structure is of recent interest because it can constrain inflation models. The joint distribution of eigenvalues of the shear field in models with primordial non-Gaussianity is derived. A useful approximation for calculations in the local non-Gaussian fnl model is provided. The modifications in the nonlinear PDF due to primordial non-Gaussianity are predicted by the same collapse models used in Gaussian statistics. An improved estimation of halo abundances in the local non-Gaussian models is found by extending the excursion set approach to include non-Gaussianity. It also highlights some implicit assumptions made in earlier studies. The effect of primordial non-Gaussianity in void abundances is also addressed.