A Framework for a Theory of Everything

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Test 26 — Dark Matter Freeze-In / Nonthermal Relic Test

If dark matter is never in thermal equilibrium with the visible sector — a "freeze-in" or other nonthermal relic — can its feeble-portal production route still match the observed relic density without overproducing radiation, warming structure beyond bounds, or accidentally thermalizing? Part of the 44-test Early Universe Granularity Test Suite, which checks whether the doctrine "cosmic history is the history of increasing recordable distinction" is consistent with standard cosmology and particle physics at each epoch — not whether it uniquely predicts that epoch.

1. Verdict

Indeterminate. The freeze-in mechanism as a generic class is well-defined, numerically self-consistent, and does not conflict with current data for a broad and well-studied range of portal couplings and masses (Hall, Jedamzik, March-Russell & West 2010; Bernal et al. 2017 review). But neither this framework nor the Standard Model supplies a specific hidden-sector field, portal operator, coupling value, or dark-matter mass to plug into that mechanism. Without a specific candidate, the abundance, free-streaming length, and lifetime cannot be computed and checked as an actual prediction — only shown, generically, to be satisfiable in principle by the freeze-in class of models. That is a real, named gap rather than a disagreement, so the honest call is Indeterminate rather than a clean agree or disagree.

2. Tested Claim

The precise claim under test: "If dark matter is produced non-thermally through a feebly-coupled portal (freeze-in / FIMP), misalignment, direct decay, gravitational production, or a phase transition — and never thermalizes with the Standard Model bath — its produced abundance can match \(\Omega_{\rm DM}h^2 = 0.120\pm0.001\) (Planck 2018) while (a) remaining cold/warm enough to satisfy free-streaming and structure-formation bounds, (b) not overproducing dark radiation beyond \(\Delta N_{\rm eff}\), and (c) not decaying too fast or too slowly relative to cosmological and astrophysical lifetime bounds." This is evaluated as a generic mechanism-consistency claim: the framework does not name a specific hidden-sector particle, portal coupling, or mass, so no specific numerical prediction is being derived or checked — only whether the class of mechanism remains viable in principle.

3. Data Used

4. Calculation Summary

Step 1 — window definition. Define the physical window \(W = \{\text{reheating through late universe},\ T_{\rm RH}\ \text{down to}\ T_0=2.7255\ {\rm K},\ \text{feeble portal coupling},\ \text{hidden sector never in chemical/kinetic equilibrium with the SM bath}\}\). This spans essentially the entire post-reheating history, unlike the sharply localized freeze-out window of a thermal WIMP.

Step 2 — granularity condition. The candidate claim is that a hidden-sector field, never thermally populated, becomes a stable, individually countable relic through one specific channel: renormalizable freeze-in (IR-dominated, abundance set by the coupling and \(m_{\rm DM}\) alone), UV freeze-in (dominated by the highest temperature reached, typically \(T_{\rm RH}\)), misalignment (axion-like), direct decay of a parent field, gravitational production (during reheating/inflaton oscillation), or a first-order phase transition. Per the procedure's Step 3 ("check that the sector never thermalizes if freeze-in is claimed"), the defining consistency condition is \(\Gamma_{\rm portal}(T) \ll H(T)\) at all times \(T \lesssim T_{\rm RH}\) — the portal interaction rate must stay below the Hubble rate throughout, which is precisely what keeps the abundance "frozen in" rather than thermalized and then frozen out.

Step 3 — rate/threshold check (generic, renormalizable IR freeze-in benchmark). For a dimension-4 portal (e.g. a Yukawa coupling \(y\) to a bath fermion/scalar), the freeze-in yield is dominated at \(T\sim m_{\rm DM}\) (IR-dominated) with comoving abundance \(Y_{\rm DM} \sim \dfrac{135\sqrt{10}}{1.66\times4\pi^{7}g_*^{3/2}}\, y^2\, M_{\rm Pl}/m_{\rm DM}\)-type scaling from a Boltzmann-equation solution as given in Hall et al. (2010); requiring \(\Omega_{\rm DM}h^2 = m_{\rm DM}\,Y_{\rm DM}\,s_0/\rho_{\rm crit}/h^2 = 0.120\) fixes \(y\sim10^{-11}\)–\(10^{-12}\) for \(m_{\rm DM}\) in the keV–TeV range (Hall et al. 2010; Bernal et al. 2017 review, their Fig. 2-3 benchmark curves). At this coupling, \(\Gamma_{\rm portal}\sim y^2 T \sim 10^{-22}\text{--}10^{-24}\,T \ll H(T)\sim T^2/M_{\rm Pl}\) is satisfied by many orders of magnitude across the relevant temperature range, confirming the sector genuinely never thermalizes — the defining self-consistency check for freeze-in.

Step 4 — structure/warmness check. A non-thermally produced relic generically has a non-thermal (often colder, sometimes hotter depending on channel) momentum spectrum compared to a thermal relic of the same mass (Merle & Totzauer 2015). Using the thermal-relic Lyman-α bound \(m_{\rm WDM}\gtrsim5.3\ {\rm keV}\) (Iršiš et al. 2017) as a reference point, IR-dominated freeze-in spectra are typically colder than a thermal relic of equal mass, so a freeze-in candidate with \(m_{\rm DM}\gtrsim{\rm few}\ {\rm keV}\) is generically consistent with structure-formation bounds; UV freeze-in or gravitational-production channels can instead be warmer and require case-by-case checking. No universal number closes this for "freeze-in in general" — it depends on the specific channel and mass, which this framework does not specify.

Step 5 — record check / cross-epoch consistency. None of the generic freeze-in benchmark points reviewed here (Hall et al. 2010; Bernal et al. 2017) violate \(N_{\rm eff}\), BBN, or \(\Omega_{\rm DM}h^2\) bounds when the coupling and mass are tuned to reproduce the observed relic density — this is by construction, since the benchmark curves are built to satisfy \(\Omega_{\rm DM}h^2=0.120\) exactly. This confirms the mechanism class is not excluded, but is silent on whether any specific realization sits inside this framework's own field content, because the framework does not specify one.

5. Granularity Interpretation

What would newly become distinguishable/recordable, if a specific freeze-in candidate were specified: a hidden-sector field that was never a resolvable, thermally-populated species (its occupation number stays parametrically small, \(f\ll1\), throughout cosmic history) would nonetheless leave a stable, individually countable relic population with a fixed comoving number density — a distinction encoded not by thermal equilibrium but by a feeble, one-way portal interaction integrated over the full expansion history. This is a genuinely different granularity route than thermal freeze-out (Test 25): the "recordable distinction" (a countable relic) appears without the sector ever crossing an equilibrium threshold. Without a named candidate, this is a statement about what the mechanism could encode, not a claim that this framework's geometry does encode it.

6. Gate Routing

Routes to the Hidden-sector weak-coupling gate in the Physics/GUT/TOE ledger:

Hidden-sector weak-coupling gate -> Indeterminate
  -> supporting calculation: generic IR-dominated freeze-in benchmark reproduces Omega_DM h^2 = 0.120 (Planck 2018)
     for portal coupling y ~ 1e-11-1e-12, m_DM ~ keV-TeV (Hall, Jedamzik, March-Russell, West 2010;
     Bernal et al. 2017); self-consistency check Gamma_portal << H(T) satisfied by many orders of magnitude
     at these couplings, confirming no thermalization; structure-formation Lyman-alpha bound (thermal-relic
     equivalent m_WDM >~ 5.3 keV, Irsic et al. 2017) is satisfiable for keV-scale-and-above freeze-in candidates;
     no N_eff or BBN conflict at the tuned benchmark points.
  -> what's missing: this framework names no hidden-sector field, portal operator, coupling value, or dark-matter
     mass of its own. The generic freeze-in mechanism is shown viable in principle; there is no specific
     candidate yet to compute an abundance, lifetime, or free-streaming length for.

7. Failure Mode

This test does not land on a clean agree or disagree, for one honest reason distinct from a data conflict:

• No named candidate. Neither this framework nor the Standard Model supplies a specific portal coupling, hidden-sector field, or dark-matter mass. The freeze-in mechanism class is shown numerically viable using literature benchmark points, but a benchmark point is not the same as an actual particle. There is simply no candidate object to test yet — for anyone.

No numerical exclusion or conflict was found for the generic mechanism, so this is not a case of the two sides disagreeing. But with no named candidate to compute a number from, it is not a clean agreement either — it is graded Indeterminate, meaning the route is plausible and unexcluded but requires more input before it can be checked either way.

8. Next Action

• Derivation (if pursued): would require identifying a specific hidden-sector field, portal operator, and coupling from this framework's own geometry (e.g., from a compactification modulus or a forced weak-coupling direction), from which \(\Omega_{\rm DM}h^2\), the free-streaming length, and the lifetime could then be computed and checked against the same bounds cited here.
• Data lookup: monitor Lyman-α and 21-cm constraints on non-thermal warm-dark-matter spectra (companion to Test 37), and CMB-S4/next-generation \(N_{\rm eff}\) sensitivity, which will tighten the dark-radiation bound used above.
• Open question, stated plainly: "a feeble coupling slowly builds up a stable relic" is a viable story, not yet a specific one; it stays a plausible route until an actual particle is named.

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