A Framework for a Theory of Everything

Test 01 — Age–Temperature Expansion Consistency Test

Does every claimed early-universe "distinction event" in the granularity story land at an age and temperature that standard expansion history actually supports? This is the first of 44 tests in the Early Universe Granularity Test Suite, and it is the load-bearing sanity check that every later test in the suite leans on.

1. Verdict

Agrees. Every claimed granularity/distinction-stabilization event listed below occurs at an age and temperature that is quantitatively consistent with the standard radiation-dominated (and, at late times, matter-dominated) expansion history. No claimed event requires a stability or binding scale that the ambient temperature at that epoch fails to support (in either direction). No claimed event contradicts BBN, CMB, or particle-physics timing constraints.

2. Tested Claim

The doctrine under test states: "Cosmic history is the history of increasing recordable distinction." Applied to timing, the specific claim audited here is: each proposed appearance of a particle, field phase, nucleus, atom, or stable record occurs at an age/temperature consistent with standard expansion history — i.e., the window \(W = \{\text{age}, \text{temperature/redshift}, \text{density/expansion regime}, \text{interactions}\}\) claimed for each transition is a window in which that transition is physically able to occur, per the Friedmann equations and the Standard Model particle content.

3. Data Used

4. Calculation Summary

For radiation domination, the standard age–temperature relation (e.g. Kolb & Turner, The Early Universe, eq. 3.36) is:

where \(g_*(T)\) is the effective number of relativistic degrees of freedom at temperature \(T\) (in MeV). Applying this relation at three benchmark epochs and comparing to the standard literature values:

For recombination, the relation is no longer purely radiation-dominated, so the Planck 2018 fitted ΛCDM value is used directly rather than the radiation-only formula: \(z_\ast = 1089.92\), giving \(T_\ast = T_{\rm CMB,0}(1+z_\ast) \approx 2.7255\,\text{K}\times1090.9 \approx 2973\,\text{K} \approx 0.256\) eV, at age \(t_\ast \approx 3.8\times10^5\) yr — matching the Planck 2018 VI Table 2 value directly (same source, not an independent check, but internally consistent).

Cross-check for BBN abundance: at \(T\approx0.08\) MeV the deuterium photodissociation bottleneck lifts (binding energy 2.22 MeV vs. photon-to-baryon ratio \(\eta\approx6\times10^{-10}\) delays the "deuterium bottleneck" from the naive \(T\sim\)2.2 MeV down to \(T\sim0.07\)–0.09 MeV) — this is the standard mechanism, reproduced here only as a plausibility check, not re-derived.

Assumptions: Standard Model particle content and \(g_*(T)\) table (no new light species beyond \(N_{\rm eff}=3.044\)); flat ΛCDM background for late-time (\(z<3400\)) epochs; natural units (\(\hbar=c=k_B=1\)) converted to seconds/Kelvin via CODATA 2018 constants.

5. Granularity Interpretation

Under the doctrine being tested, each row above corresponds to a proposed step in "increasing recordable distinction": quark–gluon plasma → confined hadrons (QCD transition) is the point past which quarks are no longer separately propagating degrees of freedom but are bound into hadronic records; neutrino decoupling is the point past which the relic neutrino background becomes (in principle) a separately propagating, non-interacting record, distinguishable from the photon bath; BBN is the point past which specific nuclear species (D, ³He, ⁴He, ⁷Li) become long-lived, countable relic abundances; recombination is the point past which neutral atoms form and the photon bath free-streams as the observable CMB — the single most information-rich "recordable distinction" in the early universe. This test does not show that the granularity framing is required by the physics — only that it is not contradicted by the timing of any of these transitions.

6. Gate Routing

Granularity timing gate — this is the gate this entire test suite is anchored to. Because Test 01 closes, it does not by itself block or license any downstream test in the suite; each of the other 43 tests (interaction-rate/Hubble decoupling, \(g_*\) ledger, causal horizon, BBN light-element abundances, CMB acoustic peaks, etc.) carries its own independent numerical check. A closure here means the coarse timeline is sound enough to host those finer-grained tests — it is a necessary consistency floor, not a substitute for them.

7. Failure Mode

Not applicable — this test closed. For completeness, the failure modes that were checked for and not found: (a) no claimed transition requires a binding/stability energy scale that exceeds the ambient thermal energy at the wrong sign (e.g., nucleons binding before nuclear binding energies exceed \(T\)); (b) no field degree of freedom was treated as an already-stable recordable particle before its actual freeze-out/decoupling time; (c) no relic abundance was asserted without pointing to the standard calculation that produces it (BBN abundances and \(N_{\rm eff}\) are treated as measured/standard-computed inputs here, not re-derived — see Data Used); (d) no cross-epoch contradiction with BBN, CMB, or \(N_{\rm eff}\) constraints was introduced.

8. Next Action

Proceed to the more granular tests in the suite that this one licenses as a floor: Test 02 (interaction rate vs. Hubble rate decoupling — the actual freeze-out criterion, of which this test only checked the coarse timing), Test 03 (the full \(g_*(T)\) ledger used here, checked degree-of-freedom by degree-of-freedom), and Test 23 (BBN light-element abundances, checked quantitatively against measured D/H and \(Y_p\) rather than only checked for timing plausibility). No distinctive derivation is claimed or required to close this test — it inherits directly from standard hot-Big-Bang cosmology.

Summary table

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