Cosmology in a simple 2+1 dimension universe

Particle physics and astrophysics tend to get closer to each other about questions associated to the position of gravitation with respect to the other fundamental interactions. That issue, which is indeed the Gordian node of today's physics, is tightly linked with problems such as the nature of dark energy and dark matter, and the possible existence of hidden additional dimensions. In the present paper, whose goal is firstly pedagogical, we will try to present the stakes and a possible way forward, via a simple model easy to visualize and which does not require long and difficult calculations. We first consider relativistic gravitation in a 2 dimension space-time (one space-like, one time-like), then we derive the cosmological consequences, and finally we outline a field theory in a full 2+1 universe (with one extra dimension). The qualitative results obtained in this simple model of universe can easily be transposed in order to better understand our usual 4-dimension space-time.