Gravitational Decays of Secluded Scalars and Graviton Dark Radiation

TL;DR

This work analyzes gravitons produced from the decay of a gravity‑coupled secluded scalar, using the dark glueball as a representative, to quantify graviton dark radiation and the resulting constraints on ΔN_eff. It develops both metric and Palatini formulations, incorporating a non‑minimal Higgs coupling ξ and trace anomaly contributions that govern decays into SM particles, and an additional φRR operator that enables φ → 2 gravitons. The authors derive decay widths into Higgs bosons, gauge bosons, and fermions (with fermionic channels suppressed before EWPT), and they quantify the graviton branching fraction B_g and its impact on ΔN_eff, finding that η with ξ ≳ O(1) can suppress graviton production in the metric case, while Palatini yields different results. They also compute the stochastic gravitational‑wave spectrum from the dark‑sector domination epoch, providing analytic expressions and showing how the spectrum depends on r = √2 c_{φ RR} m_φ^2/Λ^2, Δξ = |1 − 6ξ|, and m_φ, with potential observational implications for high‑frequency GW detectors.

Abstract

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.

Figures (6)

• Figure 1: Higgs loop induced diagram
• Figure 2: Decay channel involving SM fermions $\psi$ at the tree level
• Figure 3: Constraints on the graviton dark radiation in the $(r, \Delta \xi)$ plane, where $\Delta \xi := |1 - 6\xi|$ and $r$ is defined in Eq. \ref{['eq: r definition']}. The shaded region is excluded because it violates the bound $\Delta N_{\mathrm{eff}} \lesssim 0.19$ derived from DESI observations DESI:2024hhd. We have adopted $m_{\phi} = 3 \times 10^{13}~\mathrm{GeV}$ and $\Lambda = m_{\phi}/6$ for the benchmark values for which $T_{\mathrm{dec}} \simeq 420~\mathrm{GeV}$ even in the case of $(r, \Delta \xi) = (0, 0)$. For larger $m_\phi$, the left vertical boundary shifts slightly to smaller $r$.
• Figure 4: Comparison of the gravitational wave spectra for different combinations of $(r, \Delta \xi)$. Top: spectra for varying $\Delta \xi$ with fixed $r = 10^{-3}$. Middle: spectra for varying $r$ with fixed $\Delta \xi = 1$. Bottom: spectra for varying $r$ with fixed $\Delta \xi = 0$. We have adopted $m_{\phi} = 3 \times 10^{13}~\mathrm{GeV}$ and $\Lambda = m_{\phi}/6$, as Fig. \ref{['fig: Excluded region DR']}.
• Figure 5: Anomaly-induced interaction with fermion loop