Graviton Dark Radiation: Origins & Impact

• Graviton dark radiation is a relativistic, weakly-interacting component primarily composed of free-streaming gravitons that add to the effective radiation density (ΔN_eff).
• It arises from several early-universe mechanisms such as secluded scalar decays, primordial black hole evaporation, dark sector phase transitions, and gauge-theoretic modifications of gravity.
• Its presence modifies key cosmological observables including CMB anisotropies, BBN light-element yields, and galaxy clustering, offering insights into beyond-Standard Model physics.

Graviton dark radiation denotes a relativistic, weakly-interacting component of the universe’s energy density, comprised primarily of gravitons and/or graviton-induced relics that contribute to the effective number of relativistic species, $\Delta N_{\rm eff}$, beyond those present in the Standard Model. Models of early-universe physics predict graviton dark radiation can be generated via several mechanisms: gravitational decays of secluded heavy fields, Hawking evaporation of primordial black holes, gravitational phase transitions in dark sectors, or new gravity-mediated processes related to torsion or extra gauge freedoms in the gravitational sector. This component is directly relevant for cosmic microwave background (CMB) and big-bang nucleosynthesis (BBN) cosmology, as even subdominant graviton dark radiation can affect key observables such as the expansion history, galaxy clustering, and the inferred value of the Hubble constant.

1. Definition and Theoretical Origin

Graviton dark radiation is defined as a population of relic, free-streaming, relativistic quanta—predominantly massless spin-2 particles (gravitons)—and graviton-related excitations (including dark photons created through graviton–photon conversion). This component is “dark” in the sense that it is decoupled from the Standard Model except via gravity, thus it manifests cosmologically as an excess in the radiation energy density. Its cosmological impact is parameterized by $\Delta N_{\rm eff}$, the deviation from the Standard Model prediction for the effective number of neutrino species, which can be inferred from precise measurements of the CMB and light-element abundances.

Several models predict graviton dark radiation:

• Secluded scalar decay: Scalars from hidden sectors (e.g., dark glueballs from an $SU(N)$-confined sector), coupled only via gravity (and possibly non-minimal Higgs coupling), decay into both SM particles and pairs of gravitons. The partition of decay energy into graviton dark radiation is controlled by the particle content and coupling structure of the secluded sector (Nakayama et al., 3 Dec 2025).
• Primordial black hole evaporation: Spinning primordial black holes (PBHs) emit a Hawking radiation spectrum including gravitons. For PBHs that dominate the early universe before evaporating, gravitons constitute a non-negligible dark radiation component (Arbey et al., 2021).
• Phase transitions in dark sectors: First-order phase transitions in dark, gravitationally decoupled sectors generate stochastic gravitational-wave backgrounds. Residual light degrees of freedom and the gravitational waves themselves act as sources of dark radiation, especially when the two sectors proceed with independently conserved entropies post-transition (Nakai et al., 2020).
• Gauge-theoretic modifications of gravity: In parity-preserving, power-counting renormalizable Poincaré gauge theories with pure Yang–Mills curvature and torsion, extra boundary degrees of freedom configure an early-universe fluid with radiation-like equation of state, effectively behaving as graviton dark radiation (Barker et al., 2020).

2. Microphysical Production Mechanisms

Graviton dark radiation is generated by processes where energy stored in non-SM sectors or in exotic gravitational degrees of freedom is transferred to massless (or nearly massless) spin-2 states.

Secluded Scalar Decays: For a real scalar $\phi$ (the “dark glueball”), the decay rate into two gravitons arises from higher-dimensional curvature operators such as $$c_{\phi RR} (\phi/\Lambda) R_{\mu\nu\rho\sigma}R^{\mu\nu\rho\sigma}$$. The partial width for $\phi\to2g$ is:

$$\Gamma(\phi\rightarrow 2g) = \frac{c_{\phi RR}^2}{4\pi}\frac{m_\phi^7}{\Lambda^2 M_{\rm Pl}^4}$$

while competing decay widths into SM states are controlled by non-minimal Higgs couplings and quantum anomalies. The branching fraction to gravitons,

$$B_g \simeq \frac{r^2}{r^2 + \Delta\xi^2 + (49 \alpha_s^2)/(4\pi^2)}$$

where $r \equiv \sqrt{2} c_{\phi RR} (m_\phi^2/\Lambda^2)$ and $\Delta \xi \equiv |1-6\xi|$, quantifies the graviton dark radiation yield (Nakayama et al., 3 Dec 2025).

PBH Evaporation: Kerr (spinning) PBHs emit gravitons with greybody-modified Hawking spectra. The total graviton energy density thus produced, relative to that in SM radiation at evaporation, is

$$f_{\rm DR} = \frac{\rho_g(t_{\rm ev})}{\rho_{\rm SM}(t_{\rm ev})}$$

and translates into a present-day contribution to $\Delta N_{\rm eff}$ after redshifting with appropriate factors for changing effective relativistic degrees of freedom (Arbey et al., 2021).

Dark Sector Phase Transitions: Dark phase transitions drive the production of a stochastic GW background, and the frictionless transfer of energy into light or massless graviton degrees of freedom in a completely decoupled sector leaves residual graviton dark radiation. The abundance is set by the dark-visible temperature ratio and the number of effective dark relativistic degrees of freedom:

$$\Delta N_{\rm eff} = g_*^D \xi^4 \frac{8}{7}\left(\frac{11}{4}\right)^{4/3}$$

for entropy-conserving, non-communicating sectors (Nakai et al., 2020).

Graviton–Dark Photon Conversion: In atomic dark matter scenarios with unbroken $U(1)_\text{D}$, background dark magnetic fields mediate the conversion of propagating high-frequency gravitons into dark photons, giving rise to a new dark radiation component. The conversion is described by a two-level Schrödinger-like equation, with an oscillation frequency set by the background dark field and plasma terms (Masaki et al., 2018). The energy density in dark photons produced in this way is typically $\rho_{A'}/\rho_\text{cr} \sim 10^{-8} - 10^{-6}$, corresponding to $\Delta N_{\rm eff}\sim 10^{-3} - 10^{-2}$ for strong fields and frequencies $\gtrsim$MeV.

3. Cosmological Impact and Observational Constraints

Graviton dark radiation enters the Friedmann equations as extra radiation energy, altering the cosmic expansion rate during the radiation era and at recombination. The key observable, $\Delta N_{\rm eff}$, is constrained by CMB, BBN, and large-scale structure measurements.

Current $2\sigma$ limits from Planck+BAO+DESI are $\Delta N_{\rm eff} \lesssim 0.11$–$0.19$ (Nakayama et al., 3 Dec 2025, Arbey et al., 2021). BBN bounds on light-element yields require $\Delta N_{\rm eff} \lesssim 0.4$. Next-generation CMB experiments (e.g., CMB-S4) are projected to achieve $\sigma(N_\text{eff})\simeq0.03$, allowing for detection or exclusion of graviton dark radiation at the $0.06$ level (Nakai et al., 2020, Arbey et al., 2021).

The presence of graviton dark radiation also suppresses small-scale matter power, offering complementary probes through galaxy clustering and weak lensing.

4. Model-Dependent Features and Phenomenology

4.1 Metric vs. Palatini Formulations

In gravitational reheating scenarios with non-minimal Higgs coupling, the metric and Palatini formulations yield distinct phenomenological consequences:

• In the metric case, tuning $\xi\to1/6$ suppresses $\phi\to hh$ decays, enhancing graviton branching and potentially overproducing dark radiation unless constrained.
• In Palatini gravity, $\xi=0$ is enforced, so the graviton fraction cannot be dialed and is generically significant (Nakayama et al., 3 Dec 2025).

4.2 Gravitational-Wave Signatures

Graviton dark radiation entails a stochastic GW background whose energy density spectrum, $d\Omega_{\rm GW}/d\ln f$, encodes information on the production mechanism:

• For scalar decay, the GW spectrum peaks at $f\sim(m_\phi/2)(T_0/T_{\rm dec})$, reaching $\sim10^8$–$10^{10}$ Hz for $m_\phi\sim 10^{13}$ GeV (Nakayama et al., 3 Dec 2025).
• For dark phase transitions, peak frequencies are typically much lower, $f \sim 10^{-8}$ Hz, relevant to pulsar timing arrays (Nakai et al., 2020).

4.3 Emergent Graviton Dark Radiation in Parity-Preserving Gauge Gravity

In Poincaré Gauge Theories (PGTs) with specific coupling choices that remove explicit spatial curvature ($k$-screening), extra torsion degrees of freedom generate an effective graviton dark radiation component $\rho_{\rm dr}$, whose equation of state shifts from radiation-like in the early universe ($w=1/3$) to hot dark matter and finally to quintessence ($w\approx-0.58$) at late times. The dark radiation parameter $\Delta N_{\rm eff}$ maps directly to the initial boundary value of the torsion field at the big bang, and decays away before the late-universe observables are affected, providing both a potential solution to the Hubble tension and a natural attractor back to vanilla $\Lambda$CDM (Barker et al., 2020).

5. Analytical Framework and Mapping to $\Delta N_{\rm eff}$

All mechanisms ultimately quantify graviton dark radiation as a contribution to the total radiation density:

$$\rho_{\rm rad} = \rho_\gamma \left[1 + \frac{7}{8} \left(\frac{4}{11}\right)^{4/3} N_{\rm eff}\right]$$

with $\Delta N_{\rm eff}$ reflecting the excess above the Standard Model value.

For decay-produced gravitons,

$$\Delta N_{\rm eff} = \frac{43}{7} \left(\frac{43}{4g_*(T_{\rm dec})} \right)^{1/3} \frac{B_g}{1-B_g}$$

where $B_g$ is the branching ratio into gravitons (Nakayama et al., 3 Dec 2025).

For PBH evaporation,

$$\Delta N_{\rm eff} \simeq (8/7)(11/4)^{4/3} \, f_{\rm DR} \left[\frac{g_*(T_{RH})}{g_*(T_{EQ})}\right]\left[\frac{g_*^S(T_{EQ})}{g_*^S(T_{RH})}\right]^{4/3}$$

with $f_{\rm DR}$ the energy fraction in gravitons at reheating (Arbey et al., 2021).

For emergent torsion-induced graviton dark radiation in PGTs,

$$\Delta N_{\rm eff} \simeq \left(\varpi_r^{-2}-1\right)\frac{8}{7}\left(\frac{11}{4}\right)^{4/3}$$

parametrizing the allowed early boundary condition for the pseudoscalar torsion (Barker et al., 2020).

6. Experimental Prospects and Future Directions

Graviton dark radiation's principal cosmological signature is through modifications to $N_{\rm eff}$ observable in the CMB and BBN. High-frequency stochastic gravitational wave backgrounds associated with these mechanisms may be indirectly probed via their gravitational influence, though direct GW detection is challenging due to the high characteristic frequencies ($10^8$–$10^{10}$ Hz for reheating-induced backgrounds, $\sim 10^{-8}$ Hz for dark sector phase transitions) (Nakayama et al., 3 Dec 2025, Nakai et al., 2020). Collider and laboratory tests of gravity’s non-minimal structure (e.g., torsion coupling or non-Einsteinian corrections) also provide complementary avenues to constrain the parameters responsible for graviton dark radiation (Barker et al., 2020).

The search for dark photon flux from graviton–photon conversion and possible high-frequency gravitational wave conversion to dark radiation within strong cosmological magnetic fields (ordinary or “dark”) represent active experimental frontiers (Masaki et al., 2018).

Ongoing and future high-precision cosmological surveys (CMB-S4, DESI, and weak-lensing experiments) and next-generation efforts in gravitational-wave detection will crucially test the parameter space in which graviton dark radiation can play a cosmologically relevant role. Models predicting $\Delta N_{\rm eff}\gtrsim0.03$ will be probed to high significance, potentially revealing new gravitational sectors or falsifying concrete mechanisms for beyond-Standard-Model radiation.