IDM & iDM or the inert doublet model and inelastic dark matter

The annual modulation observed by DAMA/NaI and DAMA/Libra may be interpreted in terms of elastic or inelastic scattering of darkmatter particles. In this paper we confront these two scenarios within the framework of a very simple extension of the Standard Model, the Inert Doublet Model(IDM). In this model the dark matter candidate is a scalar, the lightest component of an extra Higgs doublet. We first revisit the case for the elastic scattering of a light scalar WIMP, M-DM similar to 10 GeV, a scenario which requires that a fraction of events in DAMA are channelled. Second we consider the possibility of inelastic Dark Matter (iDM). This option is technically natural in the IDM, in the sense that the mass splitting between the lightest and next-to-lightest neutral scalars may be protected by a Peccei-Quinn (PQ) symmetry. We show that candidates with a mass M-DM between similar to 535 GeV and similar to 50 TeV may reproduce the DAMA data and have a cosmic abundance in agreement with WMAP. This range may be extended to candidates a slight as similar to 50 GeV if we exploit the possibility that the approximate PQ symmetry is effectively conserved and that a primordial asymmetry in the dark sect or may survive until freeze-out.