## Cosmology Beyond EinsteinThis work investigates the theoretical and cosmological implications of modifying Einstein's theory of general relativity. It explores two classes of modifications to gravity: those in which the graviton is given a small mass, and those in which Lorentz invariance is spontaneously broken. It elucidates the nature of cosmological perturbations in theories of massive bimetric gravity, including a potentially deadly instability. Theories of gravity beyond general relativity could explain why the expansion of the Universe is accelerating, obviating the need for a dark energy, and can also affect the evolution of the early Universe. Next, it investigates the nature of spacetime in massive gravity theories that contain two different spacetime metrics. Lastly, the strongest constraints to date are placed on the size of Lorentz-violating effects in the gravity sector during inflation. |

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### Contents

1 | |

2 Gravity Beyond General Relativity | 21 |

Part I A Massive Graviton | 54 |

3 Cosmological Stability of Massive Bigravity | 55 |

4 Linear Structure Growth in Massive Bigravity | 71 |

5 The Geometry of DoublyCoupled Bigravity | 103 |

6 Cosmological Implications of DoublyCoupled Massive Bigravity | 117 |

7 Cosmological Implications of DoublyCoupled Massive Gravity | 135 |

8 Lorentz Violation During Inflation | 155 |

9 Discussion and Conclusions | 197 |

Appendix A Deriving the Bimetric Perturbation Equations | 207 |

Appendix B Explicit Solutions for the Modified Gravity Parameters | 212 |

Appendix C Transformation Properties of the DoublyCoupled Bimetric Action | 215 |

Appendix D EinsteinAether Cosmological Perturbation Equations in Real Space | 221 |

Appendix Curriculum Vitae | 225 |

Part II Lorentz Violation | 154 |

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A.R. Solomon acceleration æ-theory aeff aether Akrami background best-fit bimetric theory cosmic cosmological constant cosmological perturbations cosmological solutions dark energy defined degrees of freedom density derivatives discussed doubly-coupled dRGT dynamical effective metric Einstein equation equations of motion evolution expansion FLRW Friedmann equation g-metric gauge ghost-free graviton growth Hubble rate infinite-branch inflation inflaton instability interaction JCAP JHEP lapse late-time Lett limit linear linearised Lorentz invariance Lorentz symmetry Lorentz violation m/MPl massive bigravity massive gravity massless matter coupling modes no-go theorem nonlinear nonzero observations particles Phys physical Planck Planck mass potential quantum quartic equation redshift reference metric relativity Rham scalar field scale factor Schmidt-May Sect self-accelerating singly-coupled slow-roll spacetime spin-2 fields stable stress-energy tensor subhorizon symmetry Theoretical theory of gravity thesis University vacuum energy viable δφ