Probing dark energy and modified gravity with galaxy clustering and weak lensing

Abstract

The new generation of cosmological surveys, called Stage-IV surveys, provides measurements of unprecedented volume and quality. This, in turn, leads to increased statistical precision. Now our knowledge of the Universe is restricted by the efficiency of our methods and accuracy of our models, rather than by our measurements (assuming that observational systematics are fully understood). Therefore, our goal is to develop and test methods and models for analysing the data in order to reliably extract as much information as possible. We do so by extending standard modelling techniques into the nonlinear regime. We apply the nonlinear techniques to non-standard cosmological models, such as evolving and interacting dark energy models, modified gravity theories, and massive neutrinos. These alternative models attempt to resolve tensions between the cosmological parameters extracted from the early-time (high-redshift) and late-time (low-redshift) Universe, which arise in the paradigm of the standard cosmology, ΛCDM.

We refer to the measurements with which we study the laws and constituents of our Universe as cosmological probes. In this thesis we work with two cosmological probes of the late-time Universe: galaxy clustering and weak lensing. The redshifts of galaxies can be precisely measured with spectroscopic instruments. From the distribution of galaxies in redshift space we can build and then model summary statistics. Here we focus on the power spectrum and bispectrum multipoles as our main galaxy clustering observables. Regarding weak gravitational lensing, this phenomenon corresponds to the coherent distortion in the observed shapes of distant galaxies due to the bending of light by the Large Scale Structure. The degree of distortion, or shear, depends on the amount and concentration of matter along the propagation of light. Based on the measured galaxy shape distribution from photometric images, we again can build various statistics. In this thesis we focus on the cosmic shear power spectrum as our main weak lensing observable.

The goal of Chapter 1 and Chapter 2 is to provide the background information required to grasp the findings of the latter chapters. Chapter 1 familiarises the reader with the main cosmological and theoretical concepts that are necessary to understand the modelling of our main observables. We motivate our interest in the extensions of the standard cosmological model, as well as demonstrate explicitly what changes they introduce at the level of the observables. Chapter 2 establishes the notion of probability in two frameworks, Bayesian and Frequentist, that allows us to assess the accuracy of a model given the data. In the same chapter we also describe the mechanisms of the probability distribution sampling, i.e., the mechanisms of geometrically exploring the regions of the model’s parameter space that describe the data best.

In Chapter 3, we analyse the redshift space power spectrum and bispectrum multipoles of dark matter halos from a large set of simulations. Interacting dark energy, in particular the “Dark Scattering” model in which dark energy and dark matter are coupled by pure momentum exchange, is the main focus of this chapter. We find a substantial improvement of constraints on the dark energy parameters when the bispectrum multipoles are combined with the power spectrum multipoles. In Chapter 4, using the same perturbative framework, we analyse the power spectrum multipoles from a Stage-III spectroscopic survey, BOSS DR12. Now we focus on constraining a generalised parameterisation of modified gravity via the growth index and massive neutrinos. Albeit without a crucial statistical significance, we find values of the growth index which deviate from its ΛCDM limit and lead to the suppression of structure growth at late-times. Such behaviour might resolve the so-called S8 tension. In a nutshell, this cosmological tension corresponds to the contradiction between the high- and low-redshift measurements of the matter fluctuation amplitude in the standard cosmological model. Additionally, in both chapters we observe strong projection effects in the parameter space, which are pedagogically introduced in Chapter 2. We explore the projection effects in the context of spectroscopic surveys and propose possible solutions.

In Chapter 5, we develop a model-independent approach with a generalised screening function to model the nonlinear matter power spectrum for many dark energy and modified gravity models. Screening is a mechanism that allows for a theory to recover the classical gravitational interactions at small scales and in dense regions, such as our Solar System. This time we work in the halo-based reaction framework. Then, in Chapter 6, we apply this approach in the modelling of the cosmic shear power spectra. When tested on mock Stage-IV cosmic shear data, we discover promising hints of detecting the screening transition. We also explore a strong degeneracy between baryonic physics and the screening transition, as well as the impact of massive neutrinos.

In the final chapter, Chapter 7, we summarise the studies presented in this thesis and list our next steps in probing and constraining extended cosmologies with galaxy clustering and weak lensing.