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 λSS^SH^H and with the S mass entirely generated by the Higgs expectation value, has a thermally generated relic density ΩS≈0.3 if mS≈(2.9--10.5)(ΩS/0.3)1/5(h/0.7)2/50ex0exMeV. Remarkably, this is very similar to the range [mS0ex0ex=0ex0ex(6.6--15.4)η2/30ex0exMeV] required in order for the self-interaction (η/4)(S^S)² to account for self-interacting dark matter when η is not much smaller than 1. The corresponding coupling is ${{λ}}S{≈}(2.7×{}{10}^{{-}10}--3.6×{}{10}^{{-}9})({{Ω}}S/0.3{)}2/5(h/0.7{)}4/5$, implying that such scalars are very weakly coupled to the standard model sector.