Exact Calculation of Cosmological Redshift Without Dark Energy: Light Shell Expansion Model in a 3D Sphere

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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