Reconstructing Horndeski theories from cosmological observables
The nature of the accelerated expansion of the Universe remains one of the greatest challenges in modern physics. The simplest explanation is that the acceleration is driven by a cosmological constant. Large quantum corrections from the various matter fields in the Universe will contribute to the value of this constant. Unfortunately, these quantum effects lead to a discrepancy between the theoretical prediction of the rate of expansion and the observed rate by many orders of magnitude. Problems such as this have lead theorists to develop alternative models which can account for the accelerated expansion without a cosmological constant. These include the addition of an exotic matter species or even a modification to General Relativity itself. Many such theories introduce a scalar field, a concept which appears frequently in particle physics. For example, the Higgs particle is an excitation of a scalar field called the Higgs field which is a crucial component in the Standard Model of particle physics. Invoking a scalar field in cosmology adds an extra dynamical degree of freedom that can drive the accelerated expansion of the Universe, as well as introduce novel physical effects such as enhancing the clustering of matter. It is not a trivial task to include a scalar field into General Relativity as it can often lead to theoretical instabilities. There has recently been substantial interest in Horndeski theory, which is a general theory which couples the scalar field to gravity while avoiding theoretical issues. Subsets of Horndeski theory include a large range of common scalar field models such as quintessence. In order to study how the cosmological phenomenology of Horndeski theory differs from standard cosmology it is useful to have a generalised approach which enables the connection of theoretical predictions with observational data, without restricting to specific subclasses of models. The effective field theory of dark energy provides such a framework. However, the effective field theory of dark energy is purely phenomenological. In order to put constraints on Horndeski theory itself it is necessary to connect the constraints placed on the parameters in effective field theory with Horndeski theory. The aim of this thesis is to provide a method to connect constraints on cosmological parameters, soon to be measured to an unprecedented precision with the next generation of surveys, with Horndeski theory. This thesis begins with an introduction to General Relativity and cosmology before discussing models which go beyond standard cosmology. A reconstruction which maps from the effective field theory of dark energy back to the space of covariant theories is then presented. This provides a method to connect constraints on phenomenological effective field theory parameters to covariant theories. We present many applications of this reconstruction. For example, we discuss how to map from frequently utilised observational parameters to an underlying Horndeski theory. This allows one to reconstruct, for example, a Horndeski theory which exhibits a weakening of the growth of structure relative to standard General Relativity. Extending these results into the nonlinear regime is then discussed. In principle this provides the necessary tools to systematically apply stringent tests to Horndeski theory with the next generation of cosmological surveys across a broad range of length scales.