Aspects of three dimensional gravity

Gravity is the “oldest” force we know of and, at the same time the one least understood. The best theory of gravity we have thus far is General Relativity. However, there are problems with this theory at both energy scales: the infrared and the ultraviolet one. In the infrared regime, General Relativity does not explain the observed rotation curves of the galaxy and the cosmological constant problem. In the ultraviolet regime, the quantum effects start playing an important role. Such quantum effects are needed when we want to describe process that occurred immediately after the Big Bang or occur close to a black hole. The problem is that there is no theory that unifies quantum physics with General Relativity. Such a theory would be called quantum gravity.
Although there have been many attempts, no one has yet succeeded in formulating a complete, self-consistent theory of quantum gravity. Quantizing gravity faces many technical problems due to the fact that General Relativity is a complicated non-linear theory. Therefore, in it natural to look for simpler models that share the important conceptual features of General Relativity while avoiding some of the technical difficulties. One simplification is to consider General Relativity in lower dimensions: two dimensions of space and one dimension of time. Our aim is to investigate whether there are modifications of this simplified model that could improve the situation.
One modification that we consider is to assume that graviton is massive instead of massless. This could change the gravitational potential which is related with the predictions of the cosmological constant. Moreover, we consider the extensions of the massive gravity: higher spins extensions, extensions to higher dimensions and supersymmetric extensions, as well as non-relativistic gravity.