Dark Matter with Topological Defects in the Inert Doublet Model

We examine the production of dark matter by decaying topological defects in the high mass region $m_{\mathrm{DM}} \gg m_W$ of the Inert Doublet Model, extended with an extra U(1) gauge symmetry. The density of dark matter states (the neutral Higgs states of the inert doublet) is determined by the interplay of the freeze-out mechanism and the additional production of dark matter states from the decays of topological defects, in this case cosmic strings. These decays increase the predicted relic abundance compared to the standard freeze-out only case, and as a consequence the viable parameter space of the Inert Doublet Model can be widened substantially. In particular, for a given dark matter annihilation rate lower dark matter masses become viable. We investigate the allowed mass range taking into account constraints on the energy injection rate from the diffuse $γ$-ray background and Big Bang Nucleosynthesis, together with constraints on the dark matter properties coming from direct and indirect detection limits. For the Inert Doublet Model high-mass region, an inert Higgs mass as low as $\sim 200$ GeV is permitted. There is also an upper limit on string mass per unit length, and hence the symmetry breaking scale, from the relic abundance in this scenario. Depending on assumptions made about the string decays, the limits are in the range $10^{12}$ GeV to $10^{13}$ GeV.