## Structure Formation in Modified Gravity CosmologiesThis unique thesis covers all aspects of theories of gravity beyond Einstein’s General Relativity, from setting up the equations that describe the evolution of perturbations, to determining the best-fitting parameters using constraints like the microwave background radiation, and ultimately to the later stages of structure formation using state-of-the-art N-body simulations and comparing them to observations of galaxies, clusters and other large-scale structures. This truly ground-breaking work puts the study of modified gravity models on the same footing as the standard model of cosmology. Since the discovery of the accelerating expansion of the Universe, marked by the awarding of the 2011 Nobel Prize in Physics, there has been a growing interest in understanding what drives that acceleration. One possible explanation lies in theories of gravity beyond Einstein’s General Relativity. This thesis addresses all aspects of the problem, an approach that is crucial to avoiding potentially catastrophic biases in the interpretation of upcoming observational missions. |

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### Contents

1 | |

2 Linear Perturbations in Galileon Gravity Models | 23 |

3 The Observational Status of Galileon Gravity After Planck | 55 |

4 Spherical Collapse in Galileon Gravity | 91 |

5 NBody Simulations and Halo Modelling in Galileon Gravity Cosmologies | 117 |

6 Nonlinear Structure Formation in Nonlocal Gravity | 147 |

7 Lensing by Clusters and Voids in Modified Lensing Potentials | 171 |

8 Summary Conclusions and Future Work | 209 |

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amplitude Astrophys Barreira baryons best-fitting CDM model chapter CMB temperature constraints cosmic cosmological constant cosmological parameters Cubic and Quartic Cubic Galileon model Cubic model dark energy dark matter haloes dashed density field density profiles derivative DGP model errorbars expansion rate field equations fifth force Figure reproduced galaxy clusters Galileon and Nonlocal Galileon field Galileon gravity models Geff Geff/G gravitational strength gravity models halo mass function halo model impact initial conditions ISW effect lensing potential lensing signal linear halo bias linear variant matter power spectrum modifications to gravity modified gravity models N-body simulations neutrinos nonlinear structure formation Nonlocal gravity models Nonlocal model number density observational parameter space QCDM Quartic Galileon model Quartic model quasi-static Quintic R□−2R model redshift regions reproduced from Ref Roy Astron Soc scalar field screening mechanism Sheth–Tormen simulation results spherical collapse structure formation tensor values velocity WMAP