Gauge singlet scalars as cold dark matter

We consider a very simple extension of the standard model in which one or more gauge singlet scalars ${\mathit{S}}_{\mathit{i}}$ couples to the standard model via an interaction of the form ${\lambda }_{\mathit{S}}$ ${\mathit{S}}_{\mathit{i}}^{\mathrm{°}}$ ${\mathit{S}}_{\mathit{i}}$ ${\mathit{H}}^{\mathrm{°}}$H, where H is the standard model Higgs doublet. The thermal relic density of S scalars is calculated as a function of the coupling ${\lambda }_{\mathit{S}}$ and the S scalar mass ${\mathit{m}}_{\mathit{S}}$. The regions of the (${\mathit{m}}_{\mathit{S}}$,${\lambda }_{\mathit{S}}$) parameter space which can be probed by present and future experiments designed to detect scattering of S dark matter particles from Ge nuclei, and to observe upward-moving muons and contained events in neutrino detectors due to high-energy neutrinos from annihilations of S dark matter particles in the Sun and the Earth, are discussed. Present experimental bounds place only very weak constraints on the possibility of thermal relic S scalar dark matter. The next generation of cryogenic Ge detectors and of large area (${10}^4$ ${\mathrm{m}}^2$) neutrino detectors will be able to investigate most of the parameter space corresponding to thermal relic S scalar dark matter up to ${\mathit{m}}_{\mathit{S}}$≊50 GeV, while a 1 ${\mathrm{km}}^2$ detector would in general be able to detect thermal relic S scalar dark matter up to ${\mathit{m}}_{\mathit{S}}$≊100 GeV and would be able to detect up to ${\mathit{m}}_{\mathit{S}}$≊500 GeV or more if the Higgs boson is lighter than 100 GeV.