| Summary: | The ongoing quest to map the space of possible, consistent field theories, and to determine their properties, is extremely interesting from a purely theoretical perspective, as well as being a prerequisite for the phenomenological application of any such theories. To that end, this thesis is concerned with various theoretical aspects of multi-gravity theories - that is, theories which contain multiple, interacting spin-2 fields. The analysis presented here will proceed by using the Stueckelberg trick to reintroduce the multiple copies of diffeomorphism invariance which the theory would possess if none of the spin-2 fields interacted, and it is discussed in detail how to apply this to multi-gravity, and in particular how this differs from massive and bi-gravity. The structure of the interactions which arise from the helicity-0 modes of the massive gravitons is examined in the so-called decoupling limit. It is found that the structure these take in bi-gravity is generalised to that of multi-Galileons, although this is not always manifest; an extension of the so-called Galileon duality is used to probe this. Multi-gravity theories can be elegantly described using graphs to encode the network of interactions between the different fields, and this forms the basis for the other two questions which will be covered. When the theory contains a cycle of interactions, it is explicitly shown how this leads to the introduction of a ghost-like instability which is not present otherwise, and how this lowers the cutoff of the effective theory. In the absence of cycles, the structural properties of the graph which represents a given theory continue to play a large role in determining the scale at which the effective theory breaks down. This is the final topic, which is studied in detail, and upper and lower bounds on this scale are derived which depend on various properties of the graph.
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