# Alternative Models of Gravity

The theory of General Relativity has been formulated almost a century ago and has been successfully tested… in weak field regime. Already at the galactic scale, an additional unseen ingredient is necessary in order to understand the structure of the galaxy. This may either tell us that indeed there is matter that we don’t see, that doesn’t interact or that the theory of General Relativity cracks already at this scale. On another hand, extreme regime of gravity may lead to singularity, e.g. in the center of a Black Hole. There, the theory of General Relativity (GR) is expected to break down. In fact, the singularity is the signal that we are in a regime out of the validity range of GR. Alternative models of gravity are supposed to be effective models of more fundamental theories such as String Theory, Loop Quantum Gravity, Quantum effects in GR, …

There are MANY ways to modify the theory of gravity; alternative models of gravity are usually motivated from fundamental theories and/or are constructed phenomenologically and typically tested in weak field (solar system), astrophysics (binaries, gravitational waves…) and cosmology. In fact strong gravity regime is the least tested regime, it is expected that the situation changes in the next decades with the advent of gravitational wave astronomy and increase of precision and technology in electromagnetic channel.

I am interested in some classes of alternative models of gravity, in particular, those containing higher derivatives, such as Weyl Gravity or Chern Simons gravity and some other models that changes the matter/gravity coupling without additional degrees of freedom.

Note that we can distinguish two big classes of alternative models:

– those changing the dynamics of the spacetime, that is no longer described by the Einstein tensor, including additional degrees of freedom such as scalar, vector, bimetric…

– those changing the coupling of matter to spacetime, for instance, with a nonlinear coupling between the stress tensor and the Einstein tensor.

However while it is easy to modify gravity, it is very tough to modify it in a viable way, see the next few subsections.