ALP Mediated Dark Matter

• ALP-mediated dark matter is a framework where axion-like particles act as pseudo-Goldstone boson mediators between dark matter and Standard Model fields.
• The models employ effective field theory to describe diverse relic-density mechanisms such as freeze-in, decoupled freeze-out, and resonant thermal freeze-out.
• Experimental probes from beam dumps, colliders, and astrophysical observations impose stringent constraints on ALP couplings, shaping the viable parameter space.

Axion-like particle mediated dark matter denotes a class of dark-sector frameworks in which an axion-like particle (ALP), typically the pseudo-Goldstone boson of an approximate $U(1)$ global symmetry spontaneously broken at a scale $f_a$, provides the leading interaction between dark matter (DM) and Standard Model (SM) fields. In these constructions the mediator may couple to SM fermions, photons, gluons, or electroweak gauge bosons, while the dark relic abundance can arise from freeze-in, decoupled freeze-out, UV freeze-in, resonant thermal freeze-out, or other nonstandard histories rather than the standard electroweak-scale WIMP paradigm (Mutzel, 2023, Bharucha et al., 2022, Allen et al., 2024).

1. Effective field-theory structure

A representative low-energy fermionic ALP-mediator EFT introduces a pseudoscalar $a$ of mass $m_a$, a Dirac DM fermion $\chi$, and effective couplings to SM fermions, gluons, and photons,

$$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$

It is conventional to define $g_{aff}\equiv C_f/f_a$, $g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$, $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$, and $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$ (Mutzel, 2023). A closely related formulation uses a derivative ALP-DM interaction and electroweak field-strength couplings,

$f_a$0

which after electroweak symmetry breaking yields the mass-basis couplings $f_a$1, $f_a$2, $f_a$3, and $f_a$4 (Bhattacharya et al., 1 May 2025, Allen et al., 2024).

The same mediator logic appears in more specialized portals. The leptonic ALP portal couples $f_a$5 only to SM leptons and a Dirac fermion $f_a$6,

$f_a$7

with $f_a$8 and $f_a$9 (Armando et al., 2023). In the electrophilic SIMP construction, the ALP couples only to electrons and to the dark-sector fermion mass term, while the chiral EFT contains the quadratic interaction $a$0 and, for nonzero dark-sector $a$1, the cubic coupling $a$2 (Fiorentino et al., 2 Feb 2026). A further extension replaces the linear pseudoscalar portal by the quadratic coupling $a$3, where the ALP-like field $a$4 never thermalizes but still alters WIMP freeze-out through coherent forward scattering and temperature-dependent mass shifts (Ferrante et al., 20 Nov 2025).

2. Relic-density mechanisms

For number-density evolution, the basic object is the comoving abundance $a$5. In the minimal fermionic ALP-mediator setup one may write

$a$6

with collision terms from $a$7, $a$8, and $a$9 (Mutzel, 2023). When ALP-SM and ALP-DM couplings are too small for standard freeze-out, the dominant cosmologies are freeze-in from the SM bath and decoupled freeze-out (DFO) in a hidden sector with temperature $m_a$0. For $m_a$1, one study finds freeze-in roughly at $m_a$2, corresponding to $m_a$3, whereas DFO requires $m_a$4 and $m_a$5 (Mutzel, 2023). A broader beyond-freeze-out analysis finds a freeze-in region with $m_a$6, $m_a$7, and $m_a$8, while the DFO region lies at $m_a$9 and $\chi$0 (Bharucha et al., 2022).

ALP portals also realize UV freeze-in. In a Majorana-$\chi$1 model with dimension-5 ALP-SM and ALP-DM operators, the yield scales as

$\chi$2

with $\chi$3 or $\chi$4, so relic production is sensitive to the reheating temperature $\chi$5 (Ghosh et al., 2023). In a non-standard pre-BBN cosmology with $\chi$6, the abundance is suppressed as $\chi$7, and the required portal couplings are correspondingly enhanced by $\chi$8 (Ghosh et al., 2023). For $\chi$9, $$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$0, and $$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$1, the paper quotes $$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$2 and $$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$3 (Ghosh et al., 2023).

Thermal freeze-out remains viable in resonance-dominated portals. For fermionic DM annihilating through $$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$4, the near-resonance regime $$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$5 with $$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$6 yields $$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$7 for $$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$8, $$\mathcal L \supset \tfrac12(\partial_\mu a)(\partial^\mu a)-\tfrac12 m_a^2 a^2 +\sum_f \frac{C_f m_f}{f_a}\,a\,\bar f i\gamma_5 f +\frac{C_\chi m_\chi}{f_a}\,a\,\bar\chi i\gamma_5\chi +\frac{\alpha_s}{8\pi}\frac{C_G}{f_a}a\,G^a_{\mu\nu}\widetilde G^{a\mu\nu} +\frac{\alpha}{8\pi}\frac{C_\gamma}{f_a}a\,F_{\mu\nu}\widetilde F^{\mu\nu}.$$9, and $g_{aff}\equiv C_f/f_a$0 (Bhattacharya et al., 1 May 2025). In the leptonic ALP portal, the relic density is instead controlled by the $g_{aff}\equiv C_f/f_a$1-wave channel $g_{aff}\equiv C_f/f_a$2, with

$g_{aff}\equiv C_f/f_a$3

so the viable freeze-out channel is explicitly velocity suppressed at late times (Armando et al., 2023). In the electrophilic SIMP model, the dominant number-changing process is the Wess-Zumino-Witten $g_{aff}\equiv C_f/f_a$4 pion annihilation, freeze-out occurs at $g_{aff}\equiv C_f/f_a$5, and the observed relic density is obtained for $g_{aff}\equiv C_f/f_a$6 (Fiorentino et al., 2 Feb 2026).

3. Cosmological and astrophysical constraints

Cosmology is especially restrictive when ALPs are long lived or mediate visible final states. In the beyond-freeze-out fermionic scenario, very light $g_{aff}\equiv C_f/f_a$7 states can be limited by $g_{aff}\equiv C_f/f_a$8, while out-of-equilibrium ALP decays after BBN can photo-dissociate light nuclei; the same analysis states that in the DFO region the ALP is long-lived and abundantly produced, so cosmology erases most DFO parameter space (Bharucha et al., 2022). In electroweak ALP portals, Planck bounds on energy injection during recombination imply $g_{aff}\equiv C_f/f_a$9 at $g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$0, and light ALPs in equilibrium require $g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$1 few MeV or else $g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$2 excludes $g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$3 below $g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$4 (Allen et al., 2024).

Indirect detection is often driven by monochromatic or nearly monochromatic electromagnetic signatures. In electroweak-gauge-boson portals, gamma-ray line searches by Fermi-LAT, MAGIC, H.E.S.S., and archival EGRET/COMPTEL data constrain $g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$5 for $g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$6 (Allen et al., 2024). In the resonant $g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$7 freeze-out model, indirect-detection limits exclude $g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$8 few$g_{a\chi\chi}\equiv C_\chi m_\chi/f_a$9 unless the spectrum is within $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$0 of the resonance (Bhattacharya et al., 1 May 2025). This sharp dependence on $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$1 is a defining feature of photophilic ALP portals.

The electrophilic SIMP realization is constrained by both cosmology and late-time annihilation. For $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$2, the ALP decays before BBN and does not modify $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$3, but residual annihilation must satisfy $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$4 for $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$5 and $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$6 up to $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$7 (Fiorentino et al., 2 Feb 2026). The same model emphasizes that nonzero $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$8 opens an $g_{agg}\equiv (\alpha_s/8\pi)(C_G/f_a)$9-wave $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$0 channel, so heavy-ALP thermalization becomes possible only in a region that still respects these CMB and indirect-detection limits (Fiorentino et al., 2 Feb 2026).

4. Terrestrial probes: beam dumps, flavor, colliders, and direct detection

Laboratory searches are already testing portions of the ALP-mediated parameter space. In fermion-coupled ALP portals, SLAC E137 constrains production through $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$1, with non-observation implying $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$2 for $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$3; stellar cooling gives $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$4; SN1987A excludes roughly $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$5 for $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$6; rare meson decays imply $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$7 from $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$8 and $$g_{a\gamma\gamma}\equiv (\alpha/8\pi)(C_\gamma/f_a)$$9 from $f_a$00 (Mutzel, 2023). A more detailed recast of beam-dump and flavor data quotes E137 exclusions at $f_a$01 for $f_a$02, together with limits from LHCb, NA62, NA48, and CHARM in the $f_a$03 range depending on mass and visible or invisible final states (Bharucha et al., 2022).

Future intensity-frontier searches are especially relevant for UV freeze-in models because a faster pre-BBN expansion allows larger visible couplings. In the non-standard-cosmology study, future reach is quoted as $f_a$04 for DUNE ND, $f_a$05 for the LHC track-trigger, $f_a$06 for FASER 2 in the $f_a$07 range, $f_a$08 for SHiP/SBND/ICARUS in the $f_a$09 range, and $f_a$10 for DUNE$f_a$11 (Ghosh et al., 2023). This suggests that non-standard expansion histories materially alter experimental accessibility.

High-energy $f_a$12 colliders provide a complementary probe through mono-photon plus missing-energy signatures. In the photophilic fermionic portal, the signal is $f_a$13 followed by $f_a$14, with a sharp missing-energy peak because the photon energy is fixed by $f_a$15 up to beam effects (Bhattacharya et al., 1 May 2025). At $f_a$16, the cut $f_a$17 removes $f_a$18 of background while keeping almost all signal, the cut $f_a$19 rejects $f_a$20 of the remaining background at the cost of only $f_a$21 of signal, and the beam polarization choice $f_a$22 reduces the SM $f_a$23 background by a factor $f_a$24 while boosting the signal by $f_a$25 (Bhattacharya et al., 1 May 2025). For the benchmark $f_a$26, $f_a$27, $f_a$28, and $f_a$29, the significance is $f_a$30 with polarization and $f_a$31 without, while the projected coupling precision at ILC $f_a$32, $f_a$33, is $f_a$34 unpolarized and $f_a$35 with polarization (Bhattacharya et al., 1 May 2025). The electroweak ALP portal adds LEP mono-$f_a$36 and $f_a$37, LHC light-by-light scattering, inclusive diphoton, and VBF $f_a$38 probes, covering broad swathes of $f_a$39 and $f_a$40 over $f_a$41 (Allen et al., 2024).

Direct detection was long treated as negligible for pseudoscalar exchange, but a recent EFT analysis argues that this is not generally correct. Light ALPs with $f_a$42 below the typical momentum transfer lift the momentum suppression of tree-level spin-dependent scattering, while loop-induced exchange generates coherent spin-independent scattering; with flavor-changing ALP couplings to up-type quarks, the loop amplitude receives an additional top-quark-mass enhancement (Beenakker et al., 24 Nov 2025). In the benchmark EFT with $f_a$43, XENONnT excludes $f_a$44 at $f_a$45, corresponding to $f_a$46, PandaX-4T gives $f_a$47, and future DARWIN/XLZD sensitivity reaches $f_a$48 near the neutrino floor (Beenakker et al., 24 Nov 2025).

5. Celestial objects and neutron-star realizations

ALP-mediated DM has also been embedded in stellar capture and compact-object phenomenology. In one line of work, DM accumulates in neutron stars, brown dwarfs, and white dwarfs through multiscatter capture; at late times the annihilation rate saturates at $f_a$49, and the process $f_a$50 produces ALPs that escape the object and decay into gamma rays or neutrinos before reaching Earth (Klangburam et al., 2023). Using Fermi-LAT and H.E.S.S. gamma-ray data and IceCube and ANTARES neutrino data, the analysis reports exclusion of $f_a$51 down to $f_a$52 for $f_a$53 in the gamma-ray channel and $f_a$54 for $f_a$55 up to $f_a$56 in the neutrino channel, under the simplifying assumptions $f_a$57, $f_a$58, and $f_a$59 (Klangburam et al., 2023). The abstract-level summary is that gamma-ray observations can rule out ALP masses up to $f_a$60, while neutrino observations probe up to $f_a$61 (Klangburam et al., 2023).

A separate approach inserts DM and an ALP mediator directly into Quantum Hadrodynamics. In the QHD-ALP-DM framework, the relativistic mean-field equations modify the effective nucleon and DM masses through the mean field $f_a$62, and the total energy density and pressure include both hadronic and DM Fermi-sea contributions (Klangburam et al., 16 Mar 2025). The study states that typical ALP parameter values have no significant effect on the neutron-star equation of state, but increasing the DM Fermi momentum $f_a$63 or the DM mass $f_a$64 shifts the energy density to higher values while reducing the maximum mass, radius, and tidal deformability (Klangburam et al., 16 Mar 2025). The paper’s abstract reports the allowed region as $f_a$65 MeV and $f_a$66, whereas the detailed exposition gives $f_a$67 and $f_a$68; in both versions the qualitative conclusion is that multi-messenger constraints exclude sufficiently soft equations of state (Klangburam et al., 16 Mar 2025).

A later statistical study generalized this program by generating over 30,000 equations of state across $f_a$69 and $f_a$70, then filtering models with voting, likelihood, and kernel-density-estimation scores against radio and X-ray pulsars, GW170817, and HESS J1731-347 (Thakur et al., 23 Sep 2025). For the stiff hadronic baseline, the surviving region satisfies $f_a$71, with score-weighted posteriors favoring $f_a$72 and $f_a$73 with median $f_a$74 (Thakur et al., 23 Sep 2025). The same paper reports an AutoGluon regression model with $f_a$75, finding that $f_a$76 is mainly constrained by structural ratios such as $f_a$77, while $f_a$78 is set mainly by $f_a$79 (Thakur et al., 23 Sep 2025). This suggests that, in compact-star applications, ALP mediation is being used not only as a particle-physics portal but also as an effective parameterization of dark admixture in dense matter.

6. Variant portals and nonstandard dynamics

Beyond the baseline fermionic mediator picture, several specialized ALP portals have been developed. The leptonic ALP portal was proposed as a simple scenario connecting the anomalous magnetic moments to the DM relic abundance: the ALP contributes to $f_a$80 and $f_a$81 dominantly through 2-loop Barr-Zee diagrams, while the DM abundance is generated by $f_a$82-wave annihilation to ALP pairs (Armando et al., 2023). The analysis identifies a narrow viable region in which $f_a$83 and $f_a$84 few$f_a$85, with benchmark points at $f_a$86, $f_a$87, and $f_a$88 after beam-dump, collider, CMB, self-interaction, and perturbative-unitarity constraints are imposed (Armando et al., 2023).

The electrophilic ALP portal to SIMP dark pions is structurally different because the ALP maintains thermal contact with electrons rather than acting only as an $f_a$89-channel mediator. For $f_a$90, the viable region is a broad band with $f_a$91 and $f_a$92, equivalently $f_a$93 if $f_a$94 (Fiorentino et al., 2 Feb 2026). With $f_a$95, direct $f_a$96 scattering and the $f_a$97-wave channel $f_a$98 open a heavy-ALP regime with $f_a$99 up to $a$00, provided thermalization and CMB bounds are simultaneously satisfied (Fiorentino et al., 2 Feb 2026). The same paper notes that the allowed band overlaps the putative $a$01 region around $a$02 (Fiorentino et al., 2 Feb 2026).

A more radical departure from standard mediator phenomenology is the coherent freeze-out scenario. There the WIMP is coupled to a light ALP through a quadratic interaction too feeble to thermalize the ALP, but coherent forward scattering generates temperature-dependent mass shifts, the WIMP bath can spontaneously break the ALP potential at high temperature, and symmetry restoration proceeds either through a first-order phase transition or a crossover (Ferrante et al., 20 Nov 2025). In the first-order regime, delayed freeze-out permits annihilation cross sections up to two orders of magnitude above the standard value for $a$03-wave annihilation and five orders of magnitude above the standard value for $a$04-wave annihilation while still reproducing the observed relic density (Ferrante et al., 20 Nov 2025). In the crossover regime, both WIMP and ALP can contribute to DM, and the paper identifies an “ALP miracle” in which a Planck-suppressed quadratic coupling yields an ALP abundance comparable to the observed dark matter density, largely independent of its initial displacement and mass (Ferrante et al., 20 Nov 2025). This suggests that ALP-mediated dark matter is no longer restricted to weakly coupled connector models: it also includes scenarios in which the mediator reshapes the thermal history, phase structure, and even the partition of the final dark relic abundance.

Across these variants, a common pattern emerges. Freeze-in and UV freeze-in tend to favor feeble visible couplings, decoupled freeze-out requires strong hidden couplings but extremely small connector couplings, resonance-dominated freeze-out occupies narrow mass bands around $a$05, and compact-object or nonstandard-cosmology realizations shift the phenomenology toward multi-messenger astronomy and precision structure observables rather than conventional missing-energy signatures.