Probing Fundamental Cosmology with Galaxy Surveys

Abstract

The distribution of galaxies encodes a wealth of information about the early and late Universe, including its composition, initial conditions, and expansion history. Through the measurement of summary statistics such as the power spectrum and correlation functions, we can characterize the distribution, and thereby constrain the underlying parameters using likelihood analyses. This thesis considers a range of approaches for extracting information from large scale structure (LSS), extending previous works using new statistics, improved modeling, and enhanced analysis techniques. Firstly, we consider the galaxy power spectrum and bispectrum. Although many LSS analyses make use of the former statistic, few include the latter, owing to complexities in its measurement and modeling. In Part~I of this thesis, we outline new approaches to estimate such quantities, obviating previous difficulties relating to the survey window function, and in Part~II, present theoretical calculations of the power spectrum and bispectrum using the Effective Field Theory of LSS. Combining these, we can obtain precise constraints on cosmological and astrophysical parameters by fitting first-principles models to the observed statistics; in Part~III, we explore the consequences for both the standard model ($\Lambda$CDM) and its extensions, in particular inflationary theories. Amongst other topics, we can shed light on the `Hubble tension', utilizing measurements of the early-Universe `equality scale'; these results, and their cosmological interpretation, are discussed in Part~IV. The remainder of this thesis is devoted to alternative approaches to describing the galaxy distribution. Part~V considers a recently proposed statistic known as the marked power spectrum. Utilizing perturbation theory, we are able to understand its information content and purported utility, as well as derive rigorous models necessary to compare the statistic to observational data. Finally, Part~VI describes the possibility of constraining cosmology with higher-order correlation functions via the development of efficient new estimators. These provide novel tests of the standard model: we show their ability both to constrain the gravitational four-point function and to search for hints of parity-violation in the late Universe.