Thermally generated gauge singlet scalars as self-interacting dark matter

We show that a gauge singlet scalar S, with a coupling to the Higgs doublet of the form lambda(S)S(dagger)SH(dagger)H and with the S mass entirely generated by the Higgs expectation value, has a thermally generated relic density Omega(S) approximate to 0.3 if m(S) approximate to (2.9-10.5) (Omega(S)/0.3)(1/5)(h/0.7)(2/5) MeV. Remarkably, this is very similar to the range [m(S) = (6.6-15.4)eta(2/3) MeV] required in order for the self-interaction (eta/4) ((SS)-S-dagger)(2) to account or self-interacting dark matter when eta is not much smaller than 1. The corresponding coupling is lambda(S) approximate to (2.7 x 10(-10)-3.6 x 10(-9))(Omega(S)/0.3)(2/5) (h/0.7)(4/5), implying that such scalars are very weakly coupled to the standard model sector.