Probing Fundamental Physics With Galaxy Biasing

In the presence of a new generation of large-scale structure surveys, this thesis aims to discuss the method to probe the fundamental physics of inflation from galaxy distribution. In particular, the thesis reviews the introduction of the inflation model. The state-of-the-art prediction of the initial condition from inflation is computed with the cosmological perturbation theory based on the theory of General Relativity (GR). The thesis focuses on two fundamental features. Firstly, Non-Gaussianity (NG) is discussed as an indicator of physics beyond the free-single-scalar field model. Observationally, NG is realized by the non-zero bispectrum of the primordial conserved curvature perturbation. The local, equilateral, enfolded and orthogonal types of bispectrum are introduced with the associated inflation models and their mode dependence. Secondly, the parity symmetry is recognized as a fundamental discrete symmetry of the standard GR, hence the property that one would expect from the observational consequence of inflation. Essentially, the reflection of space should not alter the mechanism generating perturbations during inflation. The thesis then discusses the theory of LSS distribution, particularly how the fluctuation from inflation evolves throughout different epochs. Standard Perturbation Theory (SPT) density perturbation is employed as a method to solve the nonlinear evolution of matter fluid. The theory of biased tracer is introduced as a description of the galaxy population. The tracer number density contrast is written as an expansion of bias parameters and their corresponding physical operators representing the quantity that affects the population. This thesis shows how the list of operators up to the third order is inferred from the gravitational evolution of the tracer. The relation between the statistics of tracers as discrete objects and the statistics of continuous density field are also discussed. With this complete connection from the essence of inflation to observable LSS, the prediction of the tracer's statistics and the bias parameter can be established. The thesis reviews how the NG from inflation introduce some scale dependence to the dark matter (DM) halo bias parameter. In particular, the Matarrese-Lucchin-Bonometto (MLB) approach is reviewed. The thesis discusses the formation theory of DM halo as a virialized object enclosing smaller structure clusters of galaxies. As its position can be inferred from the clustering of galaxies, the statistics can be probed from which the bias parameters can be inferred. Therefore, such measurement can be used to constrain the level of NG in the initial condition. The dependence on the sample's halo mass and the window function based on the MLB approach is also illustrated. Lastly, the parity violation (PV) of the galaxy's four-point correlation (4PCF) function is considered. In the presence of two independent analyses (J.Hou et al. 2023 and O.H.E.Philcox 2022) findings, this thesis assesses whether the redshift space distortion (RSD) effect can mimic the PV in the observed 4PCF. While the parity-odd mode of trispectrum (the Fourier-counterpart of 4PCF) has been studied in the literature (P.Paul et al. 2024), this thesis extends the result by considering the wide-angle effect and properly correcting the local line-of-sight (LOS) for each galaxy with Taylor's expansion. It is shown in this thesis that the averaging over survey volume completely removes the PV introduced by RSD, suggesting that the isotropic 4PCF estimator used in J.Hou et al. 2023 and O.H.E.Philcox 2022 are free of such contamination. Some fundamental sources of PV and caveats are commented on.