### Abstract

The origin of the late-time acceleration of the universe is one of the biggest questions in cosmology. We give the name dark energy to the substance which is responsible for this, highlighting our ignorance on its origin. The most widely accepted explanation is that of the cosmological constant. However the naturalness of the cosmological constant, and the theoretical inconsistency with the value expected from quantum field theory, poses a question over whether this is the true explanation of the late-time acceleration. In this thesis, we investigate models of massive gravity, which arise from modifying Einsteinâ€™s theory of General Relativity, to tackle the late-time acceleration problem in a more natural way than the cosmological constant. The theories we will study are the bigravity and generalised massive gravity theories.In this work we are principally concerned with both the theoretical consistency and phenomenological implications of the aforementioned theories. To study the theoretical consistency we study cosmological perturbations and derive the stability conditions, whilst for the phenomenological study we investigate the background evolution and the effects on the large scale structure of the universe. We also investigate the screening mechanisms, which are important to allow the recovery of General Relativity on local, well tested, scales.

The first part of the thesis is dedicated to the history of massive gravity. The timeline of the development of dRGT (de-Rham, Gabadadze, Tolley) massive gravity is discussed in detail in chapter 2. The second part of chapter 2 discusses the cosmological solutions in massive gravity, and the requirement to study extensions of the theory to find stable cosmologies. We also introduce other models of massive gravity which could explain the late-time acceleration.

In chapter 3 we study the low energy limit model of bigravity. We study the linear scalar perturbations and investigate the modified Poissonâ€™s equation. To determine the details of the screening, we derive the non-linear equations and identify the Vainshtein radius. We conclude by discussing the viability of bigravity theories for dark energy.

In chapter 4 we introduce the generalised massive gravity and study its stability at the level of the quadratic action for cosmological perturbations. To do so, we derive the stability conditions as a function of the model parameters. Imposing that we require late-time acceleration and the absence of instabilities, we identify a region of parameter space in which the theory is stable. Building upon the analysis in chapter 4, we study generalised massive gravity in more detail in chapter 5. We perform a full background analysis, identifying the expansion history and equation of state of dark energy for a concrete model. Later on in chapter 5 we study the linear scalar perturbations, focusing on the effects of generalised massive gravity on large scale structure. We finish the chapter by investigating the propagation of gravitational waves and conclude the thesis with future directions and open questions in the field.

Date of Award | Mar 2021 |
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Original language | English |

Supervisor | Ahmet Emir Gumrukcuoglu (Supervisor), David Wands (Supervisor) & Kazuya Koyama (Supervisor) |