General relativity describes gravity in terms of an interacting massless spin-2 field - the graviton. This 100-year-old theory has been spectacularly successful in explaining observations. However, theoretical exploration and the cosmological constant problem motivate the study of alternative theories of gravity. Recently, there has been great progress in understanding theories that give the graviton a mass. This thesis considers several aspects of these massive spin-2 effective field theories and related theories. These theories are first studied from the perspective of scattering amplitudes. The most general 2 → 2 scattering amplitude is constructed for theories containing a single massive graviton or vector. These amplitudes are then used to find the highest strong coupling scales in such theories, assuming a particular scaling of fields and momenta. Generalisations to include additional fields and self-interactions for massive higher-spin fields are also discussed. Constraints that arise from the existence of an ultraviolet completion are then studied. It is shown using dispersion relation arguments that the pseudo-linear massive spin-2 theory cannot admit an analytic, Lorentz-invariant, and unitary ultraviolet completion, but that such completions are not ruled out for massive vector theories. The behaviour of massive spin-2 theories under dimensional reduction is also explored. Stability conditions and the lower-dimensional spectrum are derived for the Kaluza-Klein dimensional reduction of a partially massless graviton and a massive graviton on an Einstein product manifold. Additionally, the nonlinear dimensional reduction of the zero modes in dRGT massive gravity is shown to produce a mass-varying massive gravity theory. Lastly, attempts to construct a version of unimodular gravity containing a massive graviton are discussed. A candidate theory is proposed and is shown to have pathologies. Dimensional reduction is then used to generate massive spin-2 theories with noncanonical kinetic terms and auxiliary fields. These theories are shown to be equivalent to the Fierz-Pauli theory, which provides further evidence for the uniqueness of the kinetic term used in dRGT massive gravity.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:729062 |
| Date | January 2017 |
| Creators | Bonifacio, James |
| Contributors | Ferreira, Pedro ; March-Russell, John |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | https://ora.ox.ac.uk/objects/uuid:1e8bde3b-cc1a-4f09-8053-1e05fdd49d49 |
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