Was Einstein Wrong? : Theoretical and observational constraints on massive gravity

For more than a century, Einstein's theory of general relativity has described gravitational phenomena with astonishing precision. However, for the theory to fit observations we need to add two elusive substances: dark energy and dark matter. Together they add up to 95% of the energy budget of the Universe. Yet, we do not know what these substances are. Another question mark is the expansion rate of the Universe; two incompatible values are obtained depending on the measuring method. These problems (dark energy, dark matter, and the expansion rate) belong to the big questions within gravity today and they may be interpreted as signs that general relativity is not the final theory for gravity. As an alternative, in this thesis we analyze an extended theory of gravity called bimetric gravity. In general relativity (GR), gravity is massless which means that gravitational waves propagate at the speed of light. Hence, a natural extension is to consider theories where gravity has a mass. This is precisely what bimetric gravity achieves. The theoretical consistency of this theory is firmly established but it is also crucial to test if the theory agrees with observations. In fact, in this theory there are two types of gravitational waves/fields, one massless as in GR but also one massive. When observing gravitational phenomena, we observe a mix of the two. Depending on the mixing and on the mass of the massive field, observational signatures appear for example on cosmological scales, in gravitational wave events or on solar-system scales. Until recently the phenomenology of the full theory was still uncharted, and an important question was if all observational tests could be satisfied at the same time. To address this, we devised a unified framework that enables straightforward comparison between constraints from different probes, without being restricted to a particular region of the parameter space. The result is that bimetric gravity is compatible with observations and