Multiscale statistical modeling of large-scale structure: from baryon acoustic oscillations to galaxy formation histories

Abstract

This dissertation presents a comprehensive study of the large-scale structure of the Universe through two interrelated avenues: the modeling of Baryon Acoustic Oscillations (BAOs) in higher-order statistics, and the prediction of galaxy formation histories using machine learning with semi-stochastic corrections along with the validation of such models using dark matter-only simulations. The overarching goal is to improve the extraction of cosmological information and the realism of galaxy property predictions by leveraging both simulation-driven statistics and data-driven inference.

The first part (Chapters 1 and 2) focuses on modeling the BAO feature in the bispectrum—the Fourier-space analogue of the three-point correlation function. Unlike the power spectrum, the bispectrum captures non-Gaussianity and mode coupling from nonlinear gravitational evolution and galaxy bias. We develop a “wiggle-only” framework that isolates the oscillatory BAO component from the broadband bispectrum shape. Using GLAM N-body simulations (with and without BAO), we analyze signal evolution across redshifts and triangle configurations. Our aligned-template method enables percent-level recovery of the BAO dilation parameter α, accounting for template systematics. Robustness and precision are demonstrated using 1000 h⁻³ Gpc³ of realizations, showing the bispectrum’s potential to complement two-point statistics in surveys DESI and Euclid.

The second part of the thesis (Chapters 3, 4 and 5) addresses the limitations of machine learning in modeling the baryonic assembly history of galaxies within dark matter halos. Traditional models tend to smooth over short-timescale variability in star formation and chemical enrichment histories, due to their architectural bias toward minimizing global loss functions. We propose a novel correction scheme that decomposes galaxy histories in Fourier space, identifies missing high-frequency power, and re-injects statistically consistent fluctuations into the predicted histories. This framework is applied to galaxies from the IllustrisTNG simulation. The modified histories restore variability, improving accuracy on observables such as the stellar-halo mass and mass-metallicity relation, spectral energy distributions (SEDs), and photometric color distributions. The corrections particularly enhance the bimodality of galaxy colors, the scatter in metallicity at fixed mass, and the recovery of quenched populations in satellite systems. This framework is further extended to dark matter-only simulations to evaluate the generalizability of neural network-based predictions in the absence of baryonic training data. We assess the role of mass accretion history, halo concentration, and cosmic environment in enabling accurate galaxy property inference, and demonstrate how semi-stochastic corrections improve the fidelity of the generated histories.

These components address distinct but complementary aspects of large-scale structure modeling. The bispectrum-based analysis enhances the precision and robustness of cosmological distance measurements by leveraging higher-order statistics, unlocking additional information from the nonlinear regime of structure formation. In contrast, the semi-stochastic modeling of galaxy formation histories improves the realism of mock galaxy catalogs, correcting biases in data-driven predictions and enriching their utility in forward-modeling frameworks. Additionally, the thesis includes several complementary studies (Chapter 6): an angular multipole analysis of the bispectrum for probing anisotropic clustering, the mitigation of imaging systematics in galaxy survey data, and spectroscopic classification of AGN and QSO targets within DESI. Together, these efforts support the broader goal of connecting theory, simulation, and observation — advancing both the accuracy of cosmological inference and the fidelity of galaxy population modeling for current and future surveys.

Note on Chapter-End Quotations: In keeping with my roots in Odisha, India, each chapter concludes with a short quotation in Odia, my native language. These reflective excerpts are drawn from Odia literature, classical philosophy, and folk tradition, and are intended to symbolically parallel the cosmological and astrophysical ideas explored in this work. Each quote is followed by an English translation to maintain accessibility while honoring the worldview that shaped my earliest engagement with science.