Case study: the Big Bang as seen by TQNT
From the primordial beat of the spacetime weave to the freeze of matter: the birth of the universe told as a chain of equations — every step dated, quantified, and tagged with its status: theorem, derived, confronted or inherited.
What exists before anything else
Before matter, before gravity itself, there is the weave: the standing wave background of the single field χ, a gear train graduated in action whose tooth is Planck's constant. Three of the four fundamental constants pre-exist the Big Bang of matter: h (the tooth), c (the meshing, which will never know a step) and MPl (the rigidity, the clock). The fourth — G, gravity — will have to wait: it has nothing to measure as long as no mass exists.
Inflation, then the cascade
The primordial expansion follows Starobinsky's R² sector: spectral tilt ns = 1 − 2/N ≈ 0.965, very weak primordial gravitational waves (r ≈ 0.003 — LiteBIRD will decide around 2032), and an amplitude As = 1.89×10⁻⁹ obtained with no free parameter — confronted with Planck. The reheating that follows is a cascade with an exact equation of state w = 1/3: massless content on a dispersion-free weave. Nucleosynthesis is still far away — sixteen orders of magnitude of margin.
The freeze: the birth of matter
The plasma cools. At 156.5 MeV the χ condensate sets in: a network of strings of tension σχ — the single scale from which the whole mass spectrum derives — anchored in the rails, the nodal lines of the weave. Then, at a temperature derived end to end by the framework, the strings freeze:
This is the freeze: the fragmentation of the network (Nambu dynamics, exact for strings) produces closed fragments that knot themselves — the trefoil first, 59% of the knotted output. Two populations emerge: the visible (trefoils, bricks of the future baryons) and the dark reservoir — the eremnions, isolated knots too complex (c ≥ 23) to interact other than through gravity. All the matter in the universe was born within that fraction of a millisecond.
The crumb and the reservoir
The visible side is born in co-localized knot-mirror pairs — matter and antimatter in the same place — and annihilates almost entirely. What survives is the CP crumb: ηB = 7.1×10⁻¹⁰, derived at the freeze (Planck: −13%). The dark side does not annihilate: Vassiliev suppression crushes the interactions of complex knots. The dominance of dark matter is therefore not "more mass" — it is a symmetric relic facing a crumb.
The instant gravity switches on
At the freeze, knots confiscate the local undulation of the weave: the total deficit is the mass. And the weave responds to deficits — that response is gravity. So G is born in a single step, at tc:
There is no paradox with inflation operating before: the step is tautological. G is the weave's response to wells, and before the knots there is no well — nothing for G to measure. The pre-freeze dynamics belongs to the weave and its wave content; the curvature of inflation is a property of the rigidity MPl, which pre-exists.
The push: why the universe expands
The undulation each mass displaces pushes the weave. The energy budget gives back exactly the Friedmann law — expansion is no longer an initial condition, it is a mechanism:
And the vacuum residue neither dilutes nor withdraws: w = −1 by construction. Two falsifiable theorems — measured so far: Ωk = +0.0023 ± 0.0016, and DESI's preference for w(z) must regress.
Three questions the chain closes
Domain walls
Any discrete symmetry threatens to create walls that would dominate the universe (Zel'dovich's problem). Here, Z₃ triality bounds the walls by the strings: they collapse in 10⁻²³ s — nineteen orders below tc — and their energy (21 GeV per domain, already counted in the latent heat) rejoins the cascade. Dead at birth.
Antimatter walls
No antimatter islands are possible: the mirror pairs are born co-localized, annihilation is local, and the CP crumb is a constant of the dynamics — the same everywhere. The diffuse γ background constraint is passed by structure. Falsifiable: any confirmed primordial anti-helium (AMS-02) would refute.
The first magnetic field
The imperfect thermalization of the cascade (Γ/H = 0.6) guarantees gradients — hence the Biermann battery, the Seebeck of the primordial plasma: seeds of ~10⁻⁸ G comoving at the freeze. Their survival requires helicity, and the source is already in the chain: the same CP bias that makes the crumb ηB. The blazar bound is passed with a ×60,000 margin — and the loop closes, from the first primordial gradients to the supercritical field of the magnetar: the same content thermoelectricity.
The chronology
| t | T | event | status |
|---|---|---|---|
| — | — | the weave and its quartet — three present (h, c, MPl), G will be born at the freeze | theorem |
| inflation | — | Starobinsky — ns, As with no free parameter | confronted |
| reheating | ≫ BBN | cascade, w = 1/3 exact | derived |
| 16 µs | 156.5 MeV | the condensate — strings in the rails | derived |
| 0.16 ms | 62 MeV | the freeze: matter + eremnions; CP crumb; step of G | derived |
| 0.7–270 s | 1–0.07 MeV | nucleosynthesis — strictly standard | derived |
| 380 kyr | 0.26 eV | recombination — the CMB (θ* at 0.06%) | confronted |
| → today | — | push, growth, w = −1, Ωtot = 1 | theorem |
The confrontations
- Acoustic scale θ*: agreement at 0.06% (Planck SMICA); H₀ under flatness: 67.2 vs 67.4.
- ηB derived at the freeze: 7.1×10⁻¹⁰ (Planck: −13%); CMB temperature T(z): 0.1σ.
- S₈ deduced = Planck's σ₈: verified in regression (KiDS-Legacy at 0.74σ).
- Gravitational-wave background of the freeze: silence predicted — and observed (NANOGrav = astrophysics).
Honesty: the status map
Theorems: Ωtot = 1, w = −1, growth ⟹ σ₈. Derived: Tc (18 steps), ηB, the step of G. Order of magnitude: ΩDM (×4–10 within the declared uncertainties), ρΛ (123 orders resolved). Inherited — reworked, none promoted to "solved": local H₀ (distance-ladder systematics; the new JWST calibrators already give 68.4 ± 1.7), lithium-7 (stellar externality predicted), the muon puzzle (chemistry derived, pre-registered against the LHC — DOI 10.5281/zenodo.22282251). Full analysis: the TQNT monograph (Big Bang chapter).