Scalar Dark Matter candidates

We investigate the possibility that Dark Matter (dm) could be made of scalar candidates and focus, in particular, on the unusual mass range between a few MeV's and a few GeV's. After showing why the Lee-Weinberg limit (which usually forbids a dm mass below a few GeV's) does not necessarily apply in the case of scalar particles, we discuss how light candidates (mdm < O(GeV)) can satisfy both the gamma ray and relic density constraints. We find two possibilities. Either dm is coupled to heavy fermions (but if $mdm \lesssim 100$ MeV, an asymmetry between the dm particle and antiparticle number densities is likely to be required), or dm is coupled to a new light gauge boson U. The (collisional) damping of light candidates is, in some circumstances, large enough to be mentioned, but in most cases too small to generate a non linear matter power spectrum at the present epoch that differs significantly from the Cold Dark Matter spectrum. On the other hand, heavier scalar dm particles (ie with $mdm \gtrsim O(GeV)$) turn out to be much less constrained. We finally discuss a theoretical framework for scalar candidates, inspired from theories with N=2 extended supersymmetry and/or extra space dimensions, in which the dm stability results from a new discrete (or continuous) symmetry.