The model defines redshift as:

$1+z=\sin \left(\left(13.8/T\right)\cdot \pi /2\right)/\sin \left(\left(t/T\right)\cdot \pi /2\right)$

This assumes that the Big Bang (time zero) was 13.8 billion years ago.

The scale factor is:

$a\left(t\right)=\sin \left(\pi t/\left(2T\right)\right)$

At $t=T$, $a=1$, and the 3-sphere’s radius is:

$R_m=2T/\pi$

The total mass-energy is:

$M=\frac{R_m{c}^2}{2G}$

For $T=18\times {10}^9\text{years}$ (5.680368 × 10¹⁷ s):

$R_m\approx 1.083\times {10}^{26}\text{m}\approx 11.45\times {10}^9\text{light-years}$

$M\approx 7.3\times {10}^{52}\text{kg}$

The density at $t=T$, ${\rho }_{\min }$, is calculated as follows:

${\rho }_{\min }=M\left(\left(\frac{4}{3}\right)\pi R_m^3\right)\approx 1.374\times {10}^{-26}\text{kg}/{\text{m}}^{\text{3}}$

For $T=18$, the scale factor to the present time is: $\sin \left(13.8\pi /36\right)=0.9336$ and this is cubed to provide a volume difference of 0.8137, which then gives the current density in the universe as:

${\rho }_{now}=1.118\times {10}^{-26}\text{kg}/{\text{m}}^{\text{3}}$

The model assumes a finite spacetime manifold with equal curvature in space and time, motivated by special relativity’s equivalence of spatial and temporal dimensions when scaled by c. The space dimensions evolve sinusoidally with T defining the temporal scale length at $\frac{\pi }{2}$ radians. This geometry ensures a closed, boundary-free universe, where photon redshifts arise from geodesic paths.

The original model used T = 24 Gyr [4] . Fitting JWST data, including galaxies at z ≈ 14.44 (e.g., MoM z14, ~280 Myr post-Big Bang, from van Dokkum et al. (2025) [5] ), required T = 18 Gyr (2T = 36). This adjustment reflects a denser early universe, enabling more rapid formation of observed galaxies.

To refine the model, the parameter T was fitted to recent JWST observations of high-redshift galaxies, which provide precise redshift measurements for sources at z ≳ 10. Specifically, data from the CEERS survey was used from Donnan et al. (2022) [1] and the JADES program from Haro et al. (2023) [2] , including the galaxy MoM z14 at z = 14.44 ± 0.06, corresponding to an emission time of approximately 280 Myr post-Big Bang according to van Dokkum et al. (2025) [5] . A scale factor, $a\left(t\right)$, of 0.9336 × (1/15.44) = 0.0605 is implied by z = 14.44, so:

$\frac{{\rho }_{\min }}{{\left(a\left(t\right)\right)}^3}={\rho }_{\text{MoMz}14}=6.215\times {10}^{-23}\text{kg}/{\text{m}}^{\text{3}}$

Substituting $a\left(t\right)=\sin \left(\frac{\pi t}{36}\right)$

$\sin \left(\frac{\pi t}{36}\right)={\left(\frac{{\rho }_{\min }}{{\rho }_{\text{MoMz}14}}\right)}^{\frac{1}{3}}$

Solving for $t$:

$t=\frac{36}{\pi }\arcsin \left({\left(\frac{{\rho }_{\min }}{{\rho }_{\text{MoM}\text{z}14}}\right)}^{\frac{1}{3}}\right)=0.693\text{Gyr}=693\text{Myr}$

which is clearly a longer time than the previously estimated emission time of approximately 280 Myr post-Big Bang.

The fitting process employed a least-squares minimization to adjust T such that the model’s predicted redshift matches the observed redshifts of these galaxies. Using a dataset of 12 high-redshift galaxies (10 < z < 15) from JWST’s NIRSpec and NIRCam instruments, T was optimized to minimize the residual sum of squares between predicted and observed redshift. This yielded T = 18 Gyr, improving the fit for early universe sources while maintaining consistency with lower-redshift data. The redshift data, sourced from published JWST catalogs of Donnan et al. (2022) [1] and Haro et al. (2023) [2] , are publicly available, ensuring reproducibility of the fitting process.

For t ≥ 10 Gyr, the single-parameter model’s scale factor aligns with ΛCDM, using Planck parameters (H₀ = 67.32 km/s/Mpc, Ω_m = 0.3158 from Aghanim et al. (2020) [6] . Early deviations from ΛCDM, for the single-parameter model, facilitate faster structure formation. This is consistent with JWST findings.

To quantify the alignment between the model’s scale factors, the percentage difference between the normalized scale factors was calculated. This yielded the following results:

These values indicate that the scale factors align within 9%, with the difference decreasing to less than 1% as t approaches now. This close agreement validates the claim of alignment for later cosmic times, with approximate values derived from standard cosmological calculations.

The flatness problem arises from ΛCDM’s requirement that Ω ≈ 1 with extreme precision early on, according to Ryden (2016) [7] . The single-parameter model’s finite, positively curved manifold naturally maintains curvature, negating the need for fine-tuning or inflation.

The horizon problem questions the uniformity of causally disconnected CMB regions according to Ryden (2016) [7] . The finite 3-sphere ensures all points are causally connected, resolving this issue without inflation.

JWST’s high-z galaxies suggest rapid formation, see Sabti et al. (2024) [3] . The single-parameter model’s dense early universe supports efficient star formation, with galaxy formation potentially being seeded by entities similar to neutron stars. These entities can be expected to rapidly collapse into black holes, driving galaxy assembly, see Acharyya et al. (2023) [8] . The hypothesis for the existence of primordial neutron star-like entities is based on the enormously high temperature transition of the quark-gluon plasma, or QGP. Cifarelli and Bellini (2024) [9] provide the following GQP description: “The quark-gluon plasma, or QGP, is a state of matter in which quarks and gluons, the elementary building blocks of ordinary baryonic matter (as protons and neutrons), are no longer confined into hadrons by the strong force. A phase transition from ordinary nuclear matter to a QGP is expected to occur in extreme conditions of high baryon density and temperature, as is thought to have characterized the universe about 1 - 10 μs after the Big Bang or can be reached in the dense cores of neutron stars. In the laboratory, the conditions of high energy density necessary to form a QGP can be obtained by colliding heavy ions at velocities close to the speed of light”. It is therefore now hypothesized that due to the incredibly high temperatures required to sustain the QGP, the transition to hadrons can be expected to result in turbulent rotating motion so that some rotating regions may survive as stable dense entities, like neutron stars, as the universe expands beyond the point where individual neutrons are stable. Elsewhere in the universe, densities higher than those observed for neutron stars lead to the formation of black holes, so it is possible that the Einstein field equations are no longer applicable at such high densities. This implies that extrapolation beyond the density associated with neutron stars should be treated with caution.

The model can be used to predict hydrogen concentrations along photon paths from z ≥ 15 sources. JWST’s NIRSpec should analyze neutral hydrogen absorption to probe reionization, and test the model’s expansion history, see Curtis-Lake et al. (2023) [10] .

Searches for early entities, which are neutron star-like or for primordial black holes that may have formed from such entities, could confirm their role as galaxy seeds, see Yuan et al. (2024) [11] . The use of gravitational waves has also been proposed to detect primordial black holes, see Bagui et al. (2025) [12] . It is hypothesized that this seeding, together with the single-parameter model’s early density predictions, will allow observed galaxy formation timelines to be modelled using known physics. However, this would require data to support an allocation of the predicted contributions to density for the various constituents other than hydrogen, including helium, and possibly primordial neutron star-like entities or black holes.