## Infrared Non-local Modifications of General RelativityThis thesis presents significant new results on the problem of understanding the origin of dark energy in cosmology. The work develops an original approach based on modifications of General Relativity at cosmological scales, introducing non-local effective terms that can in principle emerge from fundamental local theories. Both the phenomenological consequences and theoretical aspects of the proposal are developed in depth. The thesis also contains significant new material compared to that published by the author in scientific journals. |

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### Contents

1 | |

2 Linear MasslessMassive Gauge Theories | 21 |

3 Subtleties of Nonlocal Field Theory | 81 |

4 Nonlocal Gravity | 99 |

5 Cosmology | 128 |

6 Conclusions | 149 |

Appendix A Bitensors
| 154 |

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### Common terms and phrases

action action-based model auxiliary fields background bi-tensor big rip classical components consider constraints construction corresponding cosmological constant covariant d-scalar dark energy de-Sitter defined degrees of freedom derivatives Dirian discontinuity divergence dynamical fields effective field theory effective theory equations of motion Feynman finite past flat space-time Foffa formalism future infinity gauge parameter gauge symmetry gauge theories gauge transformation gauge-invariant graviton Green’s function hiſ homogeneous solution implies initial conditions integrating-out interaction invariant inverse JCAP kinetic term latter linear Maggiore mass term massive gravity massless theory Mitsou non-dynamical fields non-linear non-local field theory non-local formulation Non-local Modifications non-local theory non-trivial operators particles path integral perturbations Phys physics projector pure-gauge quantum saturated propagator scalar mode scale spatial Stückelberg tensor transverse vacuum energy vDVZ vector Weyl Weyl tensor zero ημν μν