Perturbative and non-perturbative theories of structure formation

Abstract

Understanding the formation of structure in the Universe is one of cosmology's primary goals. The material content of the Universe is dominated by an invisible, non-baryonic component which we call dark matter. The gravitational force drives the clustering of dark matter from initially-small density fluctuations to virialised objects. At early times, and on large scales, cosmological perturbation theory (PT) provides a good model for structure formation. As local overdensities approach unity, the assumptions underlying PT start to break down. The EFTofLSS is an extension to PT which fixes some of PT's conceptual issues and makes accurate predictions in this regime. At late times, and/or on small scales, dark matter clumps collapse to form virialised structures called halos. In this non-linear regime, analytical models are approximations, and we require <em>N</em>-body simulations to accurately probe these scales. <br /> This thesis is made up of two key projects. The first of these probes the quasi-linear regime and makes conceptual inquiries into the EFTofLSS. The framework assumes that the stress tensor of the dark matter fluid may be expanded in a Maclaurin series about the overdensity and velocity fields. The coefficients of this expansion may be interpreted in two ways. In the top-down sense, they are free parameters calculable by matching the dark matter power spectrum to observations, while in the bottom-up sense they are measurable in simulations. We specialise to a one-dimensional, dark-matter only universe, where these two approaches can be directly compared. We find that the top-down and bottom-up predictions agree with each other, providing evidence for the robustness of the EFTofLSS assumptions. Additionally, we perform controlled tests that shine a light on non-linear dynamics within the EFTofLSS. <br /> The second project explores the formation of halos in the non-linear regime. The conventional analytical approach is to treat gravitational collapse with an idealised spherical model. Within the excursion-set theory framework, spherical collapse (and its ellipsoidal extension) maps the initial overdensity field of a proto-halo to its collapsed descendant. In this work, we provide an alternative to this traditional approach. Namely, we train a neural network to predict the accretion history of halos from the tidal properties of the proto-halo. We find that the neural network predicts the accretion history and derived properties of the halo population with greater accuracy than the analytical models. <br /> As cosmologists, our modelling of structure formation is incomplete. Although we are familiar with the processes that govern it, many details and nuances are yet to be fully understood. In this thesis, we have attempted to answer some open questions in this field. Through this work, we have validated the current theoretical framework to model structure formation on large scales, and introduced a novel approach to understand the formation of non-linear structures.