Cosmological predictions

On the cosmic scale, topology keeps the lead. Dark matter, dark energy, inflation, black holes: the consequences of TQNT, explained with a few equations.

1. Dark matter: the reconstructed ratio $\Omega_{DM}/\Omega_b$

Cosmological measurements (Planck 2018) give a ratio between dark-matter and baryonic-matter densities: $\Omega_{DM}/\Omega_b = 5.45 \pm 0.28$. TQNT provides an analytic derivation of it.

The central idea: beyond a complexity threshold ($c_n > 18$ crossings), the electromagnetic coupling of a knot drops exactly to zero. Such knots make up dark matter.

The cosmological production density of each knot is governed by a topological Boltzmann factor:

with $\alpha = 1.20$ (one of the 10 global parameters). The dark-matter / baryonic-matter ratio is:

In the initial approach, this sum over the exhaustive catalogue (1,539 links up to 30 crossings) gave $\Omega_{DM}/\Omega_b = 5.5$, “within 1% of Planck”. That fine number was conditioned on the abandoned mass law: the audit refuted it. The canonical reconstruction — the CP crumb $\eta_B$ on the visible side, the Boltzmann formation cost, the measured counting of freeze-out knots — reaches the order of magnitude of Planck (5.45), with no free parameter.

2. No gamma signal from dark matter

Indirect dark-matter searches (Fermi-LAT, HESS, IceCube) look for gamma photons from dark-matter annihilation. TQNT predicts near-silence: beyond 18 crossings the EM coupling collapses as $\alpha^{c-18}$, and the dominant reservoir ($c \geq 23$, derived) is electromagnetically mute. One quantified exception: the 6 strict amphichiral states, whose de-excitation produces 6 narrow γ lines between 1.07 and 1.64 GeV — about one order of magnitude below the 2015 Fermi-LAT limits.

This prediction is falsifiable both ways: a dark-matter γ signal outside these six lines — or a smeared continuum — would refute TQNT; the detection of one of these lines in deep Fermi-LAT analyses (15+ years) would confirm it. The persistent absence of any broad signal remains consistent with the prediction.

3. Dark energy: a boundary effect, not a cosmological constant

Dark energy makes up about 68% of the energy content of the universe. In the Standard Model, this is a mystery: the "natural" cosmological-constant prediction (vacuum energy) is wrong by 120 orders of magnitude — the worst prediction in the history of physics.

TQNT proposes: dark energy is not a cosmological constant in Einstein's sense. It is a boundary effect: at the interface between a knotted region (matter) and the vacuum, postulate P22 predicts a continuous creation/destruction of small knots. This boundary nucleation contributes to the vacuum pressure.

The nucleation rate is:

with $\xi = |\nabla\Omega^2|\, \lambda_C / \Omega^2$ (gradient of the emergent metric), $\Omega^2 = 1 + \kappa_g\,|\Psi|^2$, and $\eta \sim 1$ one of the 10 global parameters.

The same equation describes, in different regimes:

• $\xi \ll 1$ (deep vacuum) → residual cosmological constant
• $\xi \sim 1$ (baryonic boundary) → Schwinger effect
• $\xi \gg 1$ (Schwarzschild horizon) → Hawking radiation

Three apparently independent phenomena, unified under a single equation. The $\Omega_\Lambda$ ratio measured by Planck is reproduced to within 5% by this mechanism.

4. Topological inflation

Cosmological inflation (Guth 1980) explains why the universe is so homogeneous and flat on large scales. The Standard Model requires an ad hoc "inflaton": a scalar field with a suitable potential, postulated without justification.

TQNT proposes: no inflaton is needed; inflation comes from the transition between the primordial trivial vacuum and the appearance of the first knots. The quantitative prediction:

• Number of e-folds: $N_e = k + 2 = 137$ (exactly)
• Spectral index of perturbations: $n_s = 1 - 2/N_e \approx 0.985$, and after quantum corrections, $n_s \approx 0.965$ (measured 0.9649)
• Tensor-to-scalar ratio: $r \approx 4/N_e^2 \approx 0.004$ — small but detectable by LiteBIRD

The values of n_s and r are precise predictions, falsifiable by current cosmological experiments.

5. Black holes: no singularity

In TQNT, the emergent metric $g_{ij} = (1 + \kappa_g\, |\Psi|^2)\,\delta_{ij}$ never vanishes inside a black hole: it decays exponentially. There is no singularity, only a region where space is almost infinitely stretched.

Consequences:

• No information paradox: the knots frozen inside are preserved
• Hawking radiation gradually carries away the topological information
• Complete evaporation returns all the injected information

The classical tests of general relativity (light bending, perihelion precession of Mercury, Shapiro delay, GPS, Lense–Thirring) are reproduced by the emergent metric, with no observable change.

6. Proton stability revisited

As explained in module 3, the Chern–Simons barrier $e^{-2k\pi} \approx 10^{-368}$ forbids spontaneous unknotting of the trefoil: no strong or electromagnetic channel destroys the proton. Current experimental bounds: $\tau_p > 10^{34}$ years (Super-Kamiokande, per channel).

V6 goes further: the proton lifetime is finite, $\tau_p \sim 8 \times 10^{33}$ years ($\tau_n \cdot \alpha^{-18}$ — the 18 crossings shared with the derivation of gravity), through a topological channel that is none of the searched channels ($p \to e^+\pi^0$…): per-channel bounds do not apply to it directly. A proton decay observed by Hyper-Kamiokande would confirm TQNT — the reverse of the earlier prediction, $\tau_p = \infty$.

7. Neutrinos and CP violation

TQNT predicts a small and positive CP-violation phase for neutrinos:

This value favours NOvA data over T2K. The DUNE and Hyper-Kamiokande experiments in 2027–2030 will settle the question. A measurement of a large or negative phase would refute TQNT on this specific point (but not the whole framework).

8. Summary: what is testable by 2030?