General relativity (GR) is the standard physical theory describing gravitational interactions. All astrophysical and cosmological observations are compatible with its predictions, provided that unknown matter and energy components are included. These are called dark matter and dark energy.

In addition, GR describes the nonlinear self-interaction of a massless spin-2 field. In particle physics, there are both massless and massive fields having spin 0, 1 and 1/2. It is then well-justified to ask whether a mathematically consistent nonlinear theory describing a massive spin-2 field exists.

The Hassan–Rosen bimetric relativity (BR) is a mathematically consistent theory describing the nonlinear interaction between a massless and a massive spin-2 field. These fields are described by two metrics, out of which only one can be directly coupled to us and determines the geometry we probe.

Since it includes GR, BR is an extension of it and provides us with new astrophysical and cosmological solutions. These solutions, which may give hints about the nature of dark matter and dark energy, need to be tested against observations in order to support or falsify the theory. This requires predictions for realistic physical systems. One such system is the spherically symmetric gravitational collapse of a dust cloud, and its study is the overarching motivation behind the thesis.

Studying realistic physical systems in BR requires the solving of the nonlinear equations of motion of the theory. This can be done in two ways: (i) looking for methods that simplify the equations in order to solve them exactly, and (ii) solving the equations numerically.

The studies reviewed in the thesis provide results for both alternatives. In the first case, the results concern spacetime symmetries (e.g., spherical symmetry) and how they affect particular solutions in BR, especially those describing gravitational collapse. In the second case, inspired by the success of numerical relativity, the results initiate the field of numerical bimetric relativity. The simulations provide us with the first hints about how gravitational collapse works in BR.

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 even fit data slightly better than GR. Together with the fact that the dark energy can be explained by the interaction between the two gravitational fields, we have shown that the theory is a viable dark energy candidate. At the same time, the observational data provides a substantial restriction on the parameter space that excludes many of the popular models in the literature – an important result in and of itself.

A longstanding issue within this theory has been to predict the growth of structure while avoiding exponential instabilities. Here, we propose a simple model which solves the full, nonlinear equations of motion, which can be used to calculate the growth of structure, without any instabilities. We also describe our work towards a framework for calculating the process of gravitational collapse in this theory where we manage to solve the equations numerically for a short time interval. The results indicate that the gravitational collapse proceeds as in general relativity, assuming that the initial conditions are similar.

Future work is needed to decide whether bimetric gravity can solve any of the other big questions within gravity today, such as the discrepant expansion rate of the Universe. In this thesis, we show that it is an observationally viable dark energy candidate that exhibits novel gravitational features. In short, gravity can be massive.