Effective parent geometry
A compact Kantowski–Sachs geometry supplies an effective mass parameter M. A fully semiclassical primordial-black-hole interpretation is not yet established.
→Version 2.4 · corrected Stage-1 background
From compact
geometry to a
cosmological test.
Aeternus is a developing loop-quantum-cosmology framework testing whether an effective Kantowski–Sachs compact-object interior can pass through a quantum transition and ultimately produce an observable universe.
Working Draft v2.4 · August 2026 · Background characterized, cosmological bridge unestablished
EFFECTIVE KS GEOMETRY COLLAPSE
DIRECTIONAL EXPANSION VIABILITY OPEN
THE CENTRAL HYPOTHESIS · v2.4
A bounce is possible.
A universe is not yet proven.
Aeternus asks whether loop-quantum effects can turn gravitational collapse in a compact Kantowski–Sachs geometry into a viable cosmological expansion.
The corrected numerical result is more demanding than earlier drafts: the shear does not dilute and the angular two-sphere freezes. Aeternus must now show that this attractor exits into a low-shear, three-dimensionally expanding FLRW-like phase. Until then, the background result is scientifically interesting but the universe-genesis bridge remains unestablished.
ANIMATED CONCEPTUAL MODEL
Collapse. Bounce. Expansion.
A simplified visual of the proposed background sequence. The motion is conceptual—not a numerical spacetime simulation or a derived Penrose diagram.
01Space is squeezedKS anisotropic contraction
02Collapse stopsfinite transition · θ = 0
04The sky todayPlanck CMB reference
inside the black holetheoretical sequence →observed sky
v2.4 schematic · not to scale · Stage-1 Hamiltonian audit and KS→FLRW viability gate remain open · CMB: © ESA/Planck Collaboration
Reported Stage-1 result: a finite transition followed by a non-diluting, frozen-sphere KS attractor.
Audit required: reconcile the printed Hamiltonian, canonical variables and executed Stage-1 system.
Viability gate: demonstrate a low-shear KS-to-FLRW transition before connecting the model to the CMB.
THE REVISED AETERNUS CASCADE
What is proposed—and what is earned
Every link now carries an explicit evidentiary status. Validated background results are separated from conditional bridges and untested perturbation templates.
KS interior
Two independent scale factors encode a homogeneous but anisotropic interior and a preferred radial direction.
→Loop-quantum transition
Effective holonomy dynamics replace the classical singularity with a finite transition where Havg = 0 and dHavg/dt > 0.
→Frozen-sphere attractor
The tested post-bounce solutions lock the angular scale: H₂ = 0, while expansion continues only in the preferred radial direction.
→Cosmological viability gate
A low-shear, three-directionally expanding phase must still be demonstrated before the background can represent our universe.
REPORTED STAGE-1 BACKGROUND
The v2.4 geometric attractor
The strongest current result is not an observational prediction. It is a reported non-diluting KS attractor—and the associated negative result for isotropization.
pMeasured
0No power-law shear dilution over 41 orders of magnitude of effective-scale-factor growth.
σ/HavgMeasured
√3Persistent order-unity anisotropy, stable to seven digits across the reported window.
H₂Derived
0The angular two-sphere freezes while H₁ = 3Havg drives radial expansion.
δNKSMeasured
13.69 ± 0.1Background result only; its sign and role in a valid anisotropic bridge remain unresolved.
NEGATIVE RESULT
The corrected Stage-1 background does not isotropize: p = 0 and σ/Havg = √3. This is not an FLRW-like inflationary background. The manuscript’s Hamiltonian and its numerical implementation also require a line-by-line reconciliation before the result can be treated as independently secure.
CONDITIONAL BRIDGE ANSATZ
A useful placeholder,
not a mass prediction.
The linear form connects an effective KS parameter to a candidate suppression scale, but every load-bearing input still depends on an unbuilt anisotropic bridge and mode evolution.
k0 =αBeNeff· M
αB ≈ 0.669 assumed · Neff = 153.2 conditional · no parent-mass inversion
OBSERVATIONAL SECTOR
Candidates, open questions and a withdrawal
Version 2.4 no longer presents the former “Big Three” as completed predictions. The path to observables begins only after the background and canonical gates are cleared.
Large-scale scalar suppression
A Gaussian-like low-ℓ suppression remains a candidate template, but its amplitude is not yet derived on the measured background.
Tensor amplitude and tilt
Aeternus currently predicts neither r nor the sign of nT. Both require a regular mode calculation and defensible tensor vacuum.
Tensor-polarization asymmetry
The former potential-splitting mechanism is withdrawn. Any surviving asymmetry would have to arise from state selection.
v2.4 CRITICAL PATH
Two gates come before predictions
The immediate task is not another observational forecast. First, verify that the manuscript and code use the same KS Hamiltonian. Second, determine whether the frozen-sphere attractor can exit into a viable three-dimensional cosmology.
Discuss or review the work ↗G1Canonical auditReconcile the triads, Poisson brackets, holonomy lengths, curvature term, printed Hamiltonian and Stage-1 code.
G2Cosmological viabilityShow an exit from H₂ = 0 and σ/Havg = √3 into low-shear, three-directional expansion—or record a negative cosmological result.
G3Reproducibility packageArchive the executable equations, exact initial states, solver settings, residuals, outputs and convergence tests.
G4Bridge and perturbationsOnly after G1–G2: derive the anisotropic e-fold map, regular gauge-invariant potentials and a defensible tensor vacuum.