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 non-minimal 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 non-minimal 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.

💡 Research Summary

The paper investigates the cosmological consequences of a secluded scalar field ϕ that interacts with the Standard Model (SM) only through gravity. The authors focus on a concrete realization where ϕ is the lightest bound state (a dark glueball) of a pure hidden gauge sector with confinement scale Λ. The scalar couples to the Higgs doublet via a non‑minimal interaction ξ|H|² R̂ in the Jordan frame, and its dynamics are studied in both the metric and Palatini formulations of gravity.

After a Weyl rescaling to the Einstein frame, the metric formulation generates a derivative interaction (□ϕ)|H_c|² proportional to (1–6ξ), while the Palatini case lacks this term, effectively corresponding to ξ = 0. In addition, the trace (conformal) anomaly induces effective couplings of ϕ to the SM gauge bosons of the form ϕ F_{\muν}F^{\muν}, with coefficients set by the β‑functions of the gauge couplings. Consequently, the dominant SM decay channels are:

1. Two‑body decay into Higgs bosons: Γ(ϕ→HH) =