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 S-i couples to the standard model via an interaction of the form lambda(S)S(i)(dagger)S(i)H(dagger)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(S) and the S scalar mass ms. The regions of the (m(S),lambda(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) m(2)) neutrino detectors will be able to investigate most of the parameter space corresponding to thermal relic S scalar dark matter up to m(S) approximate to 50 GeV, while a 1 km(2) detector would in general be able to detect thermal relic S scalar dark matter up to m(S) approximate to 100 GeV and would be able to detect up to m(S) approximate to 500 GeV or more if the Higgs boson is lighter than 100 GeV