Gravitational decays of secluded scalars and graviton dark radiation

We discuss graviton dark radiation produced by the decay of a secluded scalar field that couples to the Standard Model (SM) only through gravity. Such scalar fields are long lived, and their decay channels generically include gravitons. If such particles existed and dominated the early Universe, a sizable branching ratio into gravitons would yield non-negligible dark radiation that significantly alters the subsequent thermal history of the Universe. In this work, we focus on the dark glueball as a representative secluded hidden scalar and compare the decay rates into SM particles via a nonminimal coupling to gravity with those into gravitons, paying attention to how the breaking of conformal invariance affects the amount of graviton dark radiation. We find that decays into the SM are dominated by two-body decay channels into Higgs bosons and gluons. In particular, when the Higgs field has a large nonminimal coupling to gravity, the production of graviton dark radiation is naturally suppressed in the metric formalism, and the SM sector is preferentially reheated and energy transfer to other hidden sectors is suppressed. Finally, we present the expected gravitational-wave spectrum resulting from dark glueball domination.