Exact Calculation of Cosmological Redshift Without Dark Energy: Light Shell Expansion Model in a 3D Sphere
Bibliographic record
Abstract
In this article, we present a new cosmological model based on the geometry of a finite 3D-sphere $S^3$ embedded in 4D Euclidean space, with a radius expanding linearly at the speed of light ($R = ct$). This geometry follows from a general theory where the Universe emerges as a result of a phase transition of the Higgs field from a 4D-ball $B^4$ to a 3D-sphere $S^3$. The key element of the model is the light shell expansion effect, which naturally explains additional redshift during light propagation through dynamically changing space geometry. We demonstrate that describing luminosity distances requires only two main parameters ($H_0 = 69.5 \pm 0.3$ km/s/Mpc and $\alpha = 1.47 \pm 0.01$), which provide a root-mean-square error of 4.9\% when compared with observational data ranging from local supernovae ($z < 0.01$) to the most distant JWST galaxies ($z > 13$). This is 40\% better than $\Lambda$CDM with its six parameters. The relative probability of our model against $\Lambda$CDM is $1.9 \times 10^{31}$, indicating the statistical advantage of the geometric approach. The model resolves the Hubble tension through an effective $H_0^{\text{eff}}(z)$ that varies from 73.2 km/s/Mpc locally to 69.8 km/s/Mpc in the early Universe. The age of matter, determined locally in almost flat space (13.36 billion years), agrees with the age of the oldest stars and resolves the "too old stars" problem. The model's predictions for objects with $z > 15$ can be tested with future JWST and ELT observations.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".