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A Framework for a Theory of Everything

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Early & Distant Universe › Granularity Test Suite › Test 25

Test 25 — Dark Matter Thermal Freeze-Out Test

If dark matter is a thermally-produced relic, does the standard freeze-out mechanism give the observed relic density while a specific particle candidate still survives direct-detection, indirect-detection, and collider bounds — and does the framework's "hidden-sector granularity" reading add anything to that picture beyond a relabeling of an unsolved, open experimental problem?

Open (for all of cosmology) Dark matter freeze-out
What we're checking
Observable
How much dark matter the universe ends up with — the relic density ΩDMh², set by thermal freeze-out
Standard cosmology
Ordinary freeze-out reproduces ΩDMh² = 0.12 when the annihilation cross-section sits in the classic WIMP range, ⟨σv⟩ ≈ 2.5×10⁻²⁶ cm³ s⁻¹, for a mass of ~10–1000 GeV
Granularity (consistency reading)
Runs the same freeze-out bookkeeping and lands on the same target amount — it reproduces ΩDMh² = 0.12, it does not derive it and names no particle
Measured
ΩDMh² = 0.1200 ± 0.0012 (Planck 2018) — the amount both roads reproduce
The epoch
Freeze-out at ~10⁻¹⁰ s, when annihilations can no longer keep up with the expansion (this is when the amount locks in, not the quantity being compared)
Verdict
Open (for all of cosmology) — both roads hit the same amount, but neither names the particle. The identity of dark matter is open — for everyone, not just this framework.

Here is a number the universe is oddly generous about: the amount of dark matter it made. Rewind to about a ten-billionth of a second after the Big Bang, when dark-matter particles were still being created and destroyed in equal measure inside a blazing thermal bath. As space expanded, they thinned out faster than they could find each other to annihilate — and at that instant, the freeze-out, whatever was left was frozen in for good. Standard cosmology turns the crank on that story and gets ΩDMh² = 0.12, provided the particles annihilate with a cross-section right in the historic “WIMP” range, ⟨σv⟩ ≈ 2.5×10⁻²⁶ cm³ s⁻¹. Planck measures that same 0.1200 ± 0.0012 in the sky today.

Walk in from this framework's side and you reach the same door. Its record-cost bookkeeping describes the identical freeze-out — the moment a species stops being continually remade and becomes a fixed, recordable relic — and it lands on the same target amount, 0.12. Two ways of telling the story of how much dark matter survives, agreeing on the total. That agreement is real, and it is worth stating plainly.

But hold the applause exactly where honesty demands it. Reproducing the amount is not the same as knowing what dark matter is — and here neither road can tell you. The freeze-out mechanism is generic: any of a wide family of masses (~10–1000 GeV) and couplings can hit 0.12, so matching the total pins down no specific particle, field, or coupling. This framework treats Planck's 0.12 as a measured input it consumes, not a number it derives, and it puts forward no candidate of its own. The measured amount is settled; the identity is the deep unsolved question of the whole field. So the honest verdict is not a triumphant “agrees” and not a “disagrees” either — it is Indeterminate, an open question held up in plain sight where everyone can see it.

What's going on here: two independent lines of reasoning — standard Boltzmann-equation cosmology and this framework's own bookkeeping — land on the same freeze-out mechanism and the same target number, Planck's measured dark-matter density ΩDMh² = 0.1200 ± 0.0012. Run the ordinary thermal freeze-out calculation and it reproduces that density almost exactly using a cross-section right in the historic "WIMP miracle" range. That agreement is real and it is reassuring. What's still genuinely open, plainly stated: nobody — not the Standard Model, not this framework — has identified the actual particle. The simplest weak-scale WIMP candidates are now squeezed hard by direct-detection experiments (LZ, XENONnT), so the amount of dark matter is understood while its identity is not. We're reporting that honestly rather than dressing up an experimental gap as a discovery. Agreement between two methods builds confidence in the shared calculation; it doesn't prove either framework, and it certainly doesn't tell you what dark matter is.

1. Verdict

The number, both ways

Number we’re testing
Dark-matter relic density Ω_DM h² from thermal (WIMP) freeze-out — plus whether any candidate survives detection bounds
Standard cosmology
Ordinary freeze-out reproduces Ω_DM h² = 0.12 for ⟨σv⟩ ≈ 2.5 × 10^-26 cm³ s^-1 (canonical WIMP range) at mass ~10–1000 GeV
This framework (granularity)
Runs the same freeze-out bookkeeping and lands on the same target amount — it reproduces Ω_DM h² = 0.12, it does not derive it and names no particle
Measured
Ω_DM h² = 0.1200 ± 0.0012 (Planck 2018); LZ 2024 excludes σ_SI ≳ 2.2 × 10^-48 cm² at m_χ ≈ 36 GeV; Fermi-LAT excludes canonical ⟨σv⟩ below ~100 GeV in b-bbar
Agreement
Back-of-envelope freeze-out reproduces the canonical WIMP-miracle cross-section and the measured density; but the simplest weak-scale candidates are squeezed by direct detection and no particle is named — identity open for everyone

Check the source → the calculation shown on this page (Data Used · Calculation Summary)

Indeterminate. The freeze-out mechanism itself reproduces the measured dark-matter density cleanly — standard physics and this framework agree there's no problem with the numbers. But no specific particle candidate has been confirmed: the classic weak-scale WIMP window is now largely squeezed out by direct-detection experiments, and neither the Standard Model nor this framework currently names a mass, coupling, or spin for whatever dark matter actually is. So the honest call is Indeterminate — the quantity checks out, the identity question stays open for everyone working the problem, not just for us.

2. Tested Claim

The precise claim under test: if dark matter is a thermal relic — a species that was in chemical equilibrium with the Standard-Model plasma in the early universe and "froze out" when its annihilation rate \(\Gamma = n\langle\sigma v\rangle\) fell below the Hubble expansion rate \(H(T)\) — then the freeze-out calculation must simultaneously (a) reproduce the observed cold-dark-matter density \(\Omega_{\rm DM}h^2 = 0.1200\pm0.0012\) (Planck 2018, TT,TE,EE+lowE+lensing, Planck Collaboration VI, A&A 641, A6, 2020) and (b) not be excluded by direct-detection, indirect-detection, or collider searches for the mass and coupling combination required to hit that density. The framework interprets a successful freeze-out as a "hidden-sector granularity event": a dark species becomes a stable, non-interacting (with photons), separately-recordable distinction once its number density is fixed by decoupling from the thermal bath, prior to structure formation.

3. Data Used

4. Calculation Summary

Window definition (per README Minimum Calculation 1): \(W = \{\)age \(\sim\) fraction of a second to minutes depending on mass; temperature \(T_f \sim m_\chi/20\) (standard freeze-out rule of thumb); expansion regime: radiation-dominated; relevant interaction: dark-species pair annihilation to Standard-Model states\(\}\).

Rate-vs-Hubble check (per README Minimum Calculation 3 / test-suite Step 2): the standard freeze-out condition is

\[ \Gamma_{\rm ann}(T_f) = n_\chi(T_f)\,\langle\sigma v\rangle \;\approx\; H(T_f), \qquad H(T)=\sqrt{\frac{8\pi G}{3}}\sqrt{\frac{\pi^2}{30}g_*(T)}\,T^2 . \]

Solving self-consistently for a weakly-interacting massive particle gives the well-known approximate closed-form relic-density relation (Kolb & Turner-style estimate, as used by Steigman et al. 2012):

\[ \Omega_\chi h^2 \;\approx\; \frac{3\times10^{-27}\ {\rm cm^3\,s^{-1}}}{\langle\sigma v\rangle} . \]

Setting \(\Omega_\chi h^2 = 0.1200\) (Planck 2018) and solving:

\[ \langle\sigma v\rangle \;\approx\; \frac{3\times10^{-27}}{0.12}\ {\rm cm^3\,s^{-1}} \;\approx\; 2.5\times10^{-26}\ {\rm cm^3\,s^{-1}}, \]

which matches the canonical "WIMP miracle" value quoted by Steigman, Dasgupta & Beacom (2012) to within the precision of this back-of-envelope estimate — the density-matching part of the mechanism checks out numerically using only standard freeze-out kinetics and the Planck-measured target density; no new physics from this framework enters this step.

Bounds check (per README Minimum Calculation 3 / test-suite Step 4): for the mass range where this canonical cross-section would apply (roughly \(m_\chi \sim 10\)–1000 GeV, generic s-channel or Higgs-portal-type mediator), LZ (2024) and XENONnT (2023) direct-detection limits and Fermi-LAT (2015+) indirect-detection limits together exclude the simplest thermal-WIMP realizations across most, though not all, of that mass range for generic (non-fine-tuned) mediator couplings; s-wave-suppressed, higher-mass (multi-TeV), or non-generic mediator scenarios remain open. No specific candidate mass/coupling combination is asserted or computed by this framework — this is purely a report of the current experimental state, imported wholesale from the WIMP direct/indirect-detection literature.

Cross-epoch consistency (per README Minimum Calculation 5): using the canonical thermal cross-section and mass ranges above does not perturb BBN (Test 23), \(N_{\rm eff}\) (Test 22), or the CMB acoustic structure, because a successfully-frozen-out WIMP decouples and becomes non-relativistic and non-interacting well before BBN begins (T ~ 1 MeV) for essentially the entire mass range considered (\(m_\chi \gg\) MeV) — no tension is introduced with the other closed tests in this suite.

5. Granularity Interpretation

On the framework's reading, thermal freeze-out is the epoch at which a hidden-sector species stops exchanging particle number with the visible thermal bath and its comoving number density becomes fixed — a new stable, distinguishable "distinction" (a conserved relic abundance) becomes recordable in the sense that it leaves an imprint on the subsequent expansion history and, eventually, on structure formation and possibly direct/indirect signals. This is exactly the same logical structure as neutrino decoupling (Test 22) or photon decoupling at recombination (Test 29): a species drops out of thermal contact and its properties become "frozen" as a record. The interpretive add here is only the label; the entire calculation — the Boltzmann freeze-out equation, the Planck-measured target density, and the experimental exclusion limits — is imported wholesale from standard WIMP cosmology and particle-astrophysics. No mechanism in this framework currently forces a dark-matter mass, coupling, or spin; treating any specific candidate as predicted would be overstating a result that experiment has not yet delivered.

6. Gate Routing

This test informs the dark-sector relic record gate. It is logically parallel to Test 22 (neutrino decoupling) and Test 26 (freeze-in / nonthermal relic alternative), and its downstream consistency was checked against Test 23 (BBN) per the required cross-epoch check. No GUT/TOE-level mechanism in this program currently supplies a dark-matter candidate, mass, or coupling, so there is nothing distinctive to route into the technical program beyond flagging this as an open experimental target the framework has not yet addressed.

7. Failure Mode

This test did not fail outright (no contradiction with cosmology), but it did not fully close either. The specific gap: a relic abundance calculation is available in general form (the standard freeze-out formula reproduces the Planck-measured density for a plausible, but not uniquely determined, cross-section), but no specific particle/mass/coupling candidate survives current direct-detection bounds with the generic couplings that made the "WIMP miracle" attractive in the first place. The measured value (\(\Omega_{\rm DM}h^2\)) is treated as a measurement, not something derived; the mechanism is not being confused with a confirmed particle; and no qualitative story has been substituted for the numerical density-matching and bounds checks above.

8. Next Action

Data lookup / experimental status tracking, not derivation: (a) track future LZ, XENONnT, PandaX-xT, and DARWIN direct-detection results as they push further into (or eventually fully exclude) the canonical thermal-WIMP window; (b) if the framework's technical program ever proposes a specific hidden-sector field with a computable mass and coupling, re-run this exact freeze-out and bounds check against the then- current exclusion limits rather than asserting compatibility; (c) this is an ordinary open experimental question in particle astrophysics, not something created by this framework's own machinery.

Bottom line

The thermal freeze-out mechanism, the Planck-measured target density, and the direct/indirect-detection exclusion limits all belong to standard WIMP cosmology and particle astrophysics, which this framework inherits and adds no candidate particle to. The density-match part of the calculation agrees with established cosmology; the particle-identity part is honestly Indeterminate — a real, unsolved problem in the field, and not something this program currently resolves either.

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