UC Berkeley

The next generation of cosmological surveys will measure the large-scale structure (LSS) of the universe with unprecedented statistical power, covering large cosmological volumes and yielding constraints on cosmological parameters competitive with the cosmic microwave background (CMB), letting us test the standard model of cosmology at percent levels or below across cosmic history, from the recombination era to the present. Unlike CMB experiments, which probe the early universe in the linear regime, these new surveys will map the distribution of matter and galaxies at late times where the effects of nonlinearities are significant. To reliably extract fundamental physics information from this data will require theoretical models that can make accurate predictions on large, cosmological scales while being robust against the effects of nonlinear physics of small scales, due not just to gravitational collapse but also the astrophysics of galaxy formation whose precision modeling currently eludes us.

In this dissertation we develop perturbation theory (PT) models for two key observables in upcoming surveys: the redshift-space clustering of galaxies in spectroscopic surveys and the cross correlation of galaxy clustering with weak gravitational lensing. Perturbation theory at the linear level has an indispensable role in CMB analyses, and the past decade has seen rapid developments in \textit{nonlinear} perturbation theories of large-scale structure, in part due to a reinterpretation of PT through the lens of effective field theories that has allowed for a robust and theoretically consistent treatment of the effects of non-perturbative small-scale physics on large-scale clustering. We review these developments in Chapter 1 before diving into the study of galaxy velocities and redshift-space distortions in Eulerian and Lagrangian perturbation theory (LPT) in Chapter 2. We use this knowledge to construct a model of the redshift-space galaxy 2-point function at 1-loop in perturbation theory featuring a full infrared (IR) resummation of large-scale displacements and velocities in Chapter 3. In Chapter 4, we use the same mathematical techniques to model density-field reconstruction, a technique used to sharpen the baryon acoustic oscillations (BAO) signal in spectroscopic surveys.

The PT techniques described above are quite versatile and, in Chapter 5 and 6, we use them ``out-of-the-box'' to study non-standard features in galaxy clustering due to relative perturbations between dark matter and baryons after recombination as well as exotic early-universe scenarios such as non-standard inflation and early dark energy, with a particular focus on IR resummation in LPT. In Chapter 7 we exploit this same resummation of displacements for a different purpose: by combining the perturbative Lagrangian bias expansion with exact displacements solved-for in N-body simulations we construct a model for galaxy-matter cross correlations in weak lensing surveys that significantly extend the reach of PT models without requiring any additional assumptions about the galaxy-halo connection.

To complete this dissertation, we apply the LPT models constructed in the preceding chapters to existing data in Chapters 8 and 9. In the former, we use the predictions of LPT to jointly model the ``full shape'' of pre- and post-reconstruction galaxy 2-point functions in the Baryon Oscillation Spectroscopic Survey (BOSS), showing that this combined analysis can be performed directly at the data level as opposed to the ex post facto approach of earlier analyses. In the latter, we further add in cross correlations with the weak lensing of the CMB from the Planck satellite, and, by modeling the cross correlation with the same LPT formalism as the galaxy power spectrum, do so within a consistent dynamical framework and with minimal additional parameters. Together, these pilot analyses demonstrate that the LPT formalism developed in this dissertation, and more generally perturbation theory, can offer a robust and pragmatic choice for future analyses of cosmological data, modeling the large-scale structure of the universe on cosmologically interesting scales to well within the statistical requirements set by future surveys.