The study of the large-scale structure seeks to understand the makings and evolution of the universe. In this subject, I worked on improving current techniques and their application to the existing large, high-precision cosmological data sets. Specifically, my dissertation explores boosting power spectrum measurements at large scales for 21-cm intensity maps through reconstruction, and at small scales for Lyα forest by developing and applying the optimal estimator to hundreds of high-resolution spectra.
The cosmic tidal reconstruction is a novel technique for low redshift (z < 2) 21-cm intensity mapping surveys (e.g. CHIME and HIRAX) that exploits local small-scale anisotropies due to tidal interactions. My thesis showed this algorithm is robust against redshift space distortions and can recover the signal with ~ 70% efficiency for k < 0.1 h/Mpc using N-body simulations. It also showed that if the foregrounds leak into angular modes (known as the foreground wedge), the efficiency drops down to 30–50% range. I also introduced an analytical framework based on perturbation theory, which correctly predicted the shape of the 2D power spectrum of the reconstructed field and also showed that the reconstruction mostly utilizes angular modes with k>0.3 h/Mpc.
Through absorption lines in quasar spectra, the Lyα forest technique can probe matter in vast volumes far into the past (2 < z < 5) and at smaller scales than galaxy surveys (r < 1 Mpc). 1D power spectrum of the Lyα forest (P1D) has emerged as a competitive framework to study new physics, but also has come with various challenges and systematic errors in analysis. I implemented the optimal quadratic estimator for P1D and generated synthetic spectra based on The Dark Energy Spectroscopic Instrument (DESI) specifications. Using these mock spectra, I proved robustness against relevant problems including quasar continuum errors and gaps in spectra due to bad pixels or masked high column density absorbers, showed that an input fiducial power spectrum improves the accuracy, and provided simple 5-yr forecasts for DESI P1D measurements. I applied the optimal estimator to approximately the largest data set of high-resolution Lyα quasar spectra, obtained by combining KODIAQ (HIRES), SQUAD (UVES), and XQ-100 (X-shooter). The preliminary results remarkably agree with previous measurements. This project will yield the most precise P1D measurement at small scales when completed.