The Large-Scale Structure (LSS) of the Universe, i.e. the distribution of matter and luminous tracers (such as galaxies), contains a wealth of information about the origin, composition, and evolution of the Universe. In order to extract this information, the non-linearities present in late-time observables provided by LSS surveys must be understood well. In general, there are three main sources of non-linearities: (1) non-linear matter clustering due to gravity; (2) non-linear biasing, i.e. the relation between the distribution of tracers and dark matter; and (3) primordial non-Gaussianity, which induces non-linearities in the initial conditions. The Effective Field Theory of Large-Scale Structure (EFTofLSS) provides a powerful framework to model the non-linear clustering due to gravity. In this thesis, we focus on understanding the non-linearities due to galaxy biasing using the EFTofLSS and numerical N-body simulations. This thesis is comprised of the following three projects:

In the first part, we present a novel method to constrain quadratic and cubic galaxy bias parameters in dark matter simulations. The natural statistics to constrain quadratic and cubic bias parameters are tree-level bispectrum and trispectrum, respectively. Since these statistics are computationally quite expensive, we use efficient squared and cubic field estimators that contain integrated bispectrum and trispectrum information. We use the constraints to model the one-loop halo-matter power spectrum and show that the results agree with simulations up to kmax = 0.1h Mpc 1 once an additional derivative bias is implemented (Published in: Abidi & Baldauf, JCAP07(2018)029).

In the second part, we develop a formalism to reconstruct the linear density field based on quadratic couplings in galaxy clustering. We employ a quadratic estimator inspired by Cosmic Microwave Background (CMB) lensing reconstruction. We incorporate non-linearities due to gravity, galaxy biasing and primordial non-Gaussianity, and verify our predictions with N-body simulations. We perform a Fisher matrix analysis on how the reconstructed field in combination with the biased tracer field can improve constraints on local type primordial non-Gaussianity. We find significant improvement on constraints due to cosmic variance cancellation resulting from the additional correlated modes of the reconstructed field, similar to multi-tracer analyses.

In the third part, we develop a method to constrain non-linear galaxy bias parameters using the two- and three-point functions of projected galaxy clustering in correlation with CMB lensing convergence. The project thus aims to bring the methodology developed in project 1 above closer to data. We develop the quadratic field method for projected fields to avoid complications from non-linear redshift space distortions. We perform a Fisher forecast to show that this method can indeed be used to put constraints on bias parameters and the amplitude of matter fluctuations. Finally, using N-body simulations we ascertain that the projected statistics do indeed reduce the impact of finger-of-god corrections.