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Abstract

We derive and discuss the implications of massive spin-2
fields as possible extensions of the standard theory of gravity, general relativity, in the spirit of extension
of the standard model of particle physics. We give a thorough introduction to the topic of massive
gravity from the point of view of bi- or multi-metric extensions of general relativity, focussing on the
bimetric case in the phenomenological considerations. Furthermore, known shortcomings and benefits
of such models are discussed. From this discussion it is evident that the parameter regime of interest is
mostly that of very small spin-2 masses, such that effects on galactic and extra-galactic length scales
are expected. On these grounds, we investigate the dynamics of spiral galaxies in the form of rotation
curves, from which we derive constraints on the model’s parameter space. Moreover, we discuss the
modifications of gravitational lensing by galaxy clusters, which strongly constrain these parameters.
We also highlight how these modifications could explain tentative anomalies in the observations of such
systems. Finally, we make use of the recent detection and conformation of gravitational waves. If more
than one spin-2 field is present, they are expected to mix dynamically in close analogy to the oscillation
of neutrino flavours. This observation is confirmed quantitatively, and subsequently used to derive new
constraints on the allowed masses and mixings of the two tensors. To this end, we employ both the
available data as well as a future, hypothetical sample of many such signals and their distribution as a
function of the cosmological redshift. We conclude our discussion with another critical contemplation
of the current status and provide an outlook onto possible ultraviolet completions.