Massive gravity is an extension of general relativity where the graviton, which mediates
gravitational interactions, has a non-vanishing mass. The first steps towards formulating a theory of
massive gravity were made by Fierz and Pauli in 1939, but it took another 70 years until a consistent
theory of massive gravity was written down. This thesis investigates the phenomenological
implications of this theory, when applied to cosmology. In particular, we look at cosmic expansion
histories, structure formation, integrated Sachs-Wolfe effect and weak lensing, and put constraints
on the allowed parameter range of the theory. This is done by using data from supernovae,
the cosmic microwave background, baryonic acoustic oscillations, galaxy and quasar maps and
galactic lensing.
The theory is shown to yield both cosmic expansion histories, galactic lensing and an integrated
Sachs-Wolfe effect consistent with observations. For the structure formation, however, we show
that for certain parameters of the theory there exists a tension between consistency relations for the
background and stability properties of the perturbations. We also show that a background expansion
equivalent to that of general relativity does not necessarily mean that the perturbations have to
evolve in the same way.
