Dark Glueball Domination

• Dark glueball domination is a scenario where a hidden pure Yang-Mills sector undergoes confinement, producing glueballs that can dominate the universe's energy density.
• The mechanism depends on low-energy parameters such as the confinement scale, entropy ratios, and efficient 3→2 processes that determine the relic abundance.
• This framework influences key cosmological epochs and dark matter properties, leading to observational signatures like gravitational waves and indirect detection signals.

A dark glueball domination scenario occurs when a hidden pure Yang-Mills sector, typically realized as a non-Abelian gauge group uncoupled or feebly coupled to the Standard Model (SM), evolves cosmologically such that its lightest glueball states come to dominate the energy density of the universe for a substantial epoch. In the most minimal realisations, these glueballs can constitute all or a majority of the present-day dark matter (DM). The cosmological history, relic abundance calculations, transitions between dynamical regimes, and connection to both fundamental theory and phenomenological signatures are sharply determined by a minimal set of low-energy parameters: the dark confinement scale $\Lambda$, the entropy ratio (or temperature ratio) between sectors, and model-dependent portal couplings.

1. Theoretical Framework and Cosmological Sequence

The prototypical scenario features a pure $SU(N)$ Yang-Mills sector, characterized by the Lagrangian

$$\mathcal{L} = -\frac{1}{4} G^a_{\mu\nu} G^{a\mu\nu}\,,$$

where $G^a_{\mu\nu}$ is the dark gluon field strength. As temperature drops below the dark confinement scale $\Lambda$, a first-order thermal phase transition leads to the formation of a spectrum of glueballs, the lightest of which $(J^{PC}=0^{++})$ has a mass $m_0 = \kappa\,\Lambda$ (with $\kappa\simeq6.5$ for $SU(3)$).

The early universe cosmology of such a sector branches into several regimes, depending on the reheating mechanism and sectoral temperatures:

• Canonical radiation domination: The dark and visible sectors have fixed temperature and entropy ratios set by primordial reheating, typically described by $\xi = T_d/T_{\rm vis}$ or $R = s_d/s$.
• Non-standard reheating/late entropy injection: Dominance and decay of heavy moduli, vectorlike quarks, or other out-of-equilibrium states can temporarily drive the universe into matter domination, alter the subsequent entropy ratio, and affect glueball number densities and yields (Acharya et al., 2017, Soni et al., 2017).
• Glueball-dominated era: After the confinement transition, the relic population of glueballs can redshift as matter and, depending on their abundance and lifetimes, dominate the cosmic energy density until they either decay or persist as DM (Forestell et al., 2017, Forestell et al., 2016).

The freeze-out dynamics of glueball relics is controlled by number-changing processes, most importantly $3\to2$ ("cannibal") and $2\to2$ reactions, with the $3\to2$ processes determining the residual abundance: $$\frac{dn}{dt} + 3Hn = -\langle \sigma_{3\to2} v^2 \rangle \left(n^3 - n^2 n_{\rm eq}\right)\,.$$ Freeze-out occurs when the reaction rate falls below the Hubble expansion, setting the final comoving yield $Y = n/s$ (Forestell et al., 2016). The relic density then follows as $\Omega h^2 \sim m_0 Y(s_0/\rho_c)$.

2. Regimes of Glueball Production, Freeze-Out, and Domination

The cosmological sequence and relic density are highly sensitive to the following parameters:

• Entropy/temperature ratio ($R$ or $\xi$): Fixes the relative coldness of dark glueball bath and the final relic density. $R$ is set by initial reheating or later entropy dumps (modulus decay, annihilation, etc.), and can be engineered via preferential reheating, portal strength, or decay branching ratios (Acharya et al., 2017, Halverson et al., 2016).
• Confinement scale ($\Lambda$): Determines glueball mass and interaction rates; higher $\Lambda$ increases the relic dark glueball energy density.
• Annihilation efficiency post-confinement: The efficiency of $3\to2$ reactions post–confinement distinguishes:
  • Inefficient/cold sector ($\langle\sigma v\rangle n_0 \ll H$ at formation): Yield is fixed by initial number density at confinement [(Acharya et al., 2017), regime A].
  • Efficient/hot sector ($\langle\sigma v\rangle n_0 \gg H$): Thermal equilibrium is established and the final yield is much smaller [(Acharya et al., 2017), regime B].

The relic glueball abundance enabling domination is then parametrically (Forestell et al., 2017, Carenza et al., 2024): $$\Omega_{\rm GB}h^2 \approx 0.12\,\zeta_T^{-3}\left(\frac{\Lambda}{\Lambda_0}\right)\,,\quad \zeta_T = \frac{T_{\rm dark}}{T_{\rm SM}}\,,$$ with numerical $\Lambda_0$ fixed by detailed $3\to2$ dynamics ($\sim100$–$200$ eV for $SU(3)$).

The onset of glueball domination occurs at temperature $T_{\rm dom} \sim m_0 Y$, with full matter domination if $T_{\rm dom}>T_{\rm BBN}$. This can be achieved robustly for sufficiently low $\zeta_T$ (i.e., a colder dark sector), or, equivalently, for large $\Lambda$ (Acharya et al., 2017, Halverson et al., 2016, McKeen et al., 2024).

3. Modifications from Non-Standard Cosmology and Reheating

Dark glueball domination is generic in non-standard cosmologies characterized by:

• Late time matter domination via moduli, heavy quarks, or other non-relativistic species: After the dominant matter component decays, glueballs are produced either directly in the decay or as a residual population after dilution by entropy injection (Acharya et al., 2017, Soni et al., 2017, Asadi et al., 2022).
• Altered expansion histories: Early matter domination or kination modifies the freeze-out condition by rescaling the effective Hubble rate, leading to suppression (early–MD) or enhancement (kination) of the glueball relic density (2207.13716).
• Cosmic selection rule: In scenarios where the universe undergoes a phase with heavy vectorlike quark domination before dark confinement, the final glueball abundance becomes independent of the ultraviolet scale (quark mass, initial conditions) and is determined only by the low-energy parameters $(\Lambda_d, N_d)$ (Soni et al., 2017):

$\Omega_g h^2 \propto \frac{\Lambda_d}{N_d}\,,$

subject to constraints fixing $N_d \sim \text{const}\times \Lambda_d$ for the observed DM density.

A crucial dynamical feature is that the relic glueball density in such histories depends only weakly on detailed microphysics or initial conditions, but is set predominantly by the ratios of decay widths and sectoral branching fractions (Acharya et al., 2017, Soni et al., 2017).

4. Constraints and Phenomenological Implications

The viability of dark glueball domination depends on several cosmological and observational bounds:

• Self-interaction constraints: For $m_{\rm glueball}\lesssim100$ MeV, dark glueball self-interactions are strong ($\sigma/m\gtrsim1\,\mathrm{cm}^2/\mathrm{g}$), violating astrophysical constraints on dark matter structure (Acharya et al., 2017, Carenza et al., 2024).
• Lifetime bounds and decay: Glueball decay via portal operators (dimension-6 Higgs, dimension-8 gauge) can lead to observable and often excluded signatures if decay occurs during or after BBN (require $\tau\lesssim0.1$ s), recombination (CMB distortions), or the present epoch (indirect detection, $\gamma$-rays) (Forestell et al., 2017, Carenza et al., 2024, Curtin et al., 2022, Asadi et al., 2022, Nakayama et al., 3 Dec 2025).
• Overclosure: If the relic density from glueballs exceeds observed dark matter abundance, the universe is overclosed, ruling out the corresponding region of $(\Lambda, \xi)$ parameter space. For "democratic" reheating ($\xi=1$), even $\Lambda\gtrsim$ eV can lead to overclosure unless the sector is sufficiently diluted or glueballs are allowed to decay sufficiently early (Halverson et al., 2016).
• Gravitational wave signals: Glueball domination and subsequent decays (especially via gravitational portals) can source a primordial gravitational wave background, with a characteristic high-frequency ($\gtrsim$ GHz–THz) broken power-law spectrum, and extra dark radiation ($\Delta N_{\rm eff}$), constrained by CMB and BBN (Nakayama et al., 3 Dec 2025).

A summary of selected parameter dependencies is given below.

Quantity	Expression	Significance
Lightest glueball mass	$m_0\approx(6-7)\Lambda$	Lattice determined for $SU(3)$
Relic density scaling	$$\Omega_{\rm GB} h^2\sim \zeta_T^{-3} \Lambda/\Lambda_0$$	Sets DM abundance
Domination temperature	$T_{\rm dom}\sim m_0\, Y$	Onset of matter domination
Self-interaction bound	$m_0\gtrsim120\ \mathrm{MeV}$	$\sigma/m\lesssim 1\,\mathrm{cm}^2/\mathrm{g}$
Decay width (dim-6 Higgs)	$\Gamma\sim m_0^5/M^4$	Glueball lifetime

For sufficiently high $\Lambda$, efficient $3\to2$ depletion, and/or cold dark sector ($\zeta_T\ll1$), observed DM abundance can be matched (McKeen et al., 2024, Carenza et al., 2024, 2207.13716). Conversely, models with overproduction must invoke dilution (entropy injections), late-time decays, or alternative cosmological histories to remain viable (Halverson et al., 2016, Acharya et al., 2017, Asadi et al., 2022).

5. Model Variants and Extensions: Portals, Composite ALPs, and Laboratory Signatures

Several model classes predict or exploit dark glueball domination:

• Minimal pure-Yang-Mills dark sectors: No portal to the SM, stable glueballs via accidental symmetry (Curtin et al., 2022, Carenza et al., 2024). Glueball DM abundance is set solely by sectoral cooling ($\xi$, $R$), $\Lambda$, and $3\to2$ rates.
• Glueball-ALPs (GALPs): If dimension-8 operators couple glueballs to photons/gluons, phenomenology maps onto that of composite axion-like particles, but with distinctive mass ranges, effective decay constants, and viable parameter windows (Carenza et al., 2024, Carenza et al., 2024). The decay constants can be super-Planckian, and the mass range extends from hundreds of MeV to TeV or higher.
• Connector-induced scenarios: Portal operators enable glueball decay, affecting cosmological observables, enabling entropy dilution (glueball-induced early matter domination), or making glueballs accessible through indirect detection or long-lived particle collider searches (Bishara et al., 2024, Asadi et al., 2022, Nakayama et al., 3 Dec 2025).
• Gravitationally-coupled or modulus reheating: Late modulus decay sets the hidden-to-visible entropy ratio and reheating temperature, enabling larger $\Lambda$ and less severe entropy suppression compared to standard high-$T_R$ cosmologies (Acharya et al., 2017, Nakayama et al., 3 Dec 2025). This can relax the otherwise strict requirement for a "cold" dark sector.

Phenomenologically, glueball domination impacts early structure formation, CMB, large-scale structure, BBN, and may be testable via indirect and gravitational-wave observations, as well as at next-generation long-lived particle detectors (Bishara et al., 2024).

6. Parameter Dependence, Constraints, and Model-Building Implications

The allowed parameter ranges for glueball domination are determined by ensuring consistency with observed $\Omega_{\rm DM}$, limits from self-interaction and decay lifetimes, and avoidance of overclosure and excessive dark radiation. Typical viable regions for $SU(3)$, depending on the portal and reheating scenario, are:

• Confinement scale $\Lambda\sim 100\ \mathrm{eV}$–$10^5\ \mathrm{GeV}$.
• Sectoral temperature ratio $\zeta_T\sim 0.1$–$0.5$ for heavy dark matter candidates.
• Portal suppression scales $M\gtrsim10^8\ \mathrm{GeV}$ (dim-6) or $M\gtrsim10^9\ \mathrm{GeV}$ (dim-8) to achieve long glueball lifetimes as DM.
• Baryon masses (in squeezed-out/diluted scenarios) as high as $10^6$–$10^7$ TeV if sufficient entropy is injected by glueball decay (Asadi et al., 2022).

In string-motivated scenarios containing many hidden Yang-Mills sectors, consistency with cosmological constraints is highly nontrivial due to the potential for overproduction in each sector, unless preferential reheating or prompt glueball decay is invoked (Halverson et al., 2016).

The following points summarize the conditions for glueball dark matter domination:

• Entropy injection must be engineered (e.g., via modulus or heavy particle decay) to adjust the $\zeta_T$ ratio as needed.
• Portal operators must be sufficiently suppressed to ensure glueball longevity, unless intentional decay and entropy dilution is desired.
• Glueball mass / self-interaction constraints must be respected to ensure consistency with astrophysical data.
• Overproduction is avoided only for specific $\Lambda$ and $\zeta_T$ or by invoking non-standard thermal histories.
• Composite dynamics impose "cosmic selection rules" where the observed relic is set by IR parameters, independent of UV scales and initial conditions for significant periods of early matter domination (Soni et al., 2017).

7. Phenomenological and Observational Signatures

Dark glueball domination and its aftermath have distinctive phenomenological implications:

• Early matter domination and entropy injection: Alters the thermal history, suppresses small-scale structure, allows for ultra-heavy dark baryons, and can delay or accelerate cosmological milestones relative to standard cosmology (Asadi et al., 2022, Bishara et al., 2024).
• Gravitational waves: Late-time decay of dominating glueballs, especially via gravitationally-coupled portals, produces high-frequency gravitational wave backgrounds with broken power-law spectra; in certain realizations thermal graviton production is also significant (Nakayama et al., 3 Dec 2025).
• Indirect detection: Decaying glueballs (e.g., via dimension-8 operators) generate astrophysical signals across a wide energy range, potentially yielding $\gamma$-rays, cosmic rays, or cosmic microwave/hard X-ray backgrounds (Carenza et al., 2024, Curtin et al., 2022).
• Long-lived particle searches: Glueballs produced in exotic Higgs decays or other new-physics processes can be probed directly at colliders via displaced vertices or missing energy signatures (Bishara et al., 2024).
• Astrophysical impact: Dark glueball interactions affect the formation and structure of halos, the substructure of DM, and possibly stellar cooling and supernova energetics, especially for glueball–ALP models (Carenza et al., 2024, Carenza et al., 2024).

Collectively, these signatures make dark glueball domination, and hidden sector Yang-Mills dynamics in general, a rich area for both cosmological and experimental investigation, yielding sharp non-trivial constraints and predicting distinctive flows of energy and structure in the early universe.