In the standard model of cosmology (LCDM) we have the presence of two unknown components, namely the dark matter and the dark energy. Normally, within the standard model, these two components interact only gravitationally, so their conservation equations holds independently. On the other hand, as we don’t have a fundamental theory about them yet, there is no need to rule out any other form of interaction, so it is instructive to study how this affects the cosmological equations.
Another motivation is that interaction helps to alleviate the cosmological constant and the coincidence problems. The cosmological constant problem is about the huge difference between the observed value of Λ and the theoretical one. In the most severe version we need a fine tuning of about 120 orders of magnitude.
The coincidence problem question the similar observed value of the dark energy and dark matter densities. We know that in the standard model these two components evolve differently (dark energy is constant and dark matter decays with a-3 ), so, why today they
have this similar value?
As an example we will show a particular model of interaction based in the work of Chen and Wu (1990).