THE 4-SPHERE MODEL: INTRODUCTION

Recent JWST detections — including the JADES GS z14 0 galaxy at \(z \approx 14.3\) — place unexpected pressure on FLRW based distance and age estimates, as such systems appear markedly more massive and more evolved than the cosmic ages predicted by the standard metric would allow.

This motivates a re examination of the conceptual foundations linking expansion, redshift, and cosmological geometry. Here I explore an alternative framework in which the Universe is modeled as the three dimensional surface of a hypersphere \((S^3)\) expanding at a constant rate, with radius \(r=ct\). In this scenario, matter appears as a discontinuity within a geometry governed by the CMB, preserving Hubble’s law while offering a finite yet unbounded Universe without invoking dark matter or dark energy. The model introduces a distinct interpretation of galactic recession and provides testable predictions through supernova distance measurements, including those accessible with JWST.

Its broader implications concern global energy, the relation between entropy conservation and reversibility, the dynamical role of BAO and the CMB, the status of the cosmological constant and its correlation with quantum field theoretic results in the hyperspherical context, and the gravity–expansion balance encoded in the Hyperspherical Expansion Acceleration (HEA).

The model further introduces a General Methodology—applicable in both Special Relativity and FLRW contexts—that enables the validation or falsification of its predictions through supernova distance measurements. This includes the use of JWST photometric filters, converted into rest frame Johnson B and V bands via transmission curve analysis, allowing a direct comparison with established supernova datasets.

From a macroscopic perspective, the model relies on the physical laws and principles that govern the observable Universe; from a microscopic viewpoint, it considers only the particles currently known to the Standard Model. To provide a clear and organized roadmap of the research, the relevant literature has been structured across Zenodo and viXra. The theoretical core and recent advancements are detailed in the Zenodo preprints, while the standalone empirical validations and observational case studies are hosted on viXra.

Consolidated Publications & Core Framework

I am pleased to share the latest developments of my \(S^3\) hyperspherical cosmology, hereafter, the 4-Sphere model. Although the treatment is not exhaustive, I have aimed to present the framework as clearly and accurately as possible through a sequence of focused articles. The definitive and updated versions of my research have now been consolidated on Zenodo and viXra. For readers interested in the broader context and in the most scientifically accurate formulation of the model, the relevant repository links are provided below.

Note on Links: All the links below point directly to the Zenodo and viXra versioning pages, ensuring you always have access to the latest, corrected revisions.

Theoretical Framework (Hosted on Zenodo): The list below represents the recommended reading order.

  1. Dynamics on an Expanding Hypersphere: Reassessing the Cosmological Principle in light of the CMB
  2. The Vacuum Catastrophe revisited: when the quantum vacuum does not contribute to cosmological equilibrium
  3. The Aporia of Reversibility in Cosmological Expansion
  4. Ancient orbital structures: simulating Local Group evolution under full Hyperspherical Expansion Acceleration
  5. A new perspective on Hubble’s law through a four-dimensional spatial model
  6. Reevaluating the Necessity of Dark Matter and Dark Energy within Cosmological Models
  7. Non Keplerian MW–M31 dynamics under Hyperspherical Expansion Acceleration: a bound solution without Dark matter

The broader implications of this speculative framework rest on the empirical robustness of Hubble’s law and the independent validation of stellar distances, but also on a set of necessary assumptions—discussed in the cited works—that remain conjectural. These include the predominant dynamical role of BAO and the CMB, a reconsideration of the Cosmological Principle, the status of the cosmological constant in its relation to Quantum Field Theory, the restoration of the link between entropy conservation and reversibility. Matter as a discontinuity implies the model’s global energy conservation associated with the CMB alone. Conversely, the gravity–expansion balance encoded in the newly introduced Hyperspherical Expansion Acceleration (HEA) imposes the non-conservative energy \(E_{HEA}\) of matter.

A separate line of investigation addresses the consequences of this framework for the interpretation of Dark Matter and Dark Energy, as developed in the dedicated study listed above.

Case studies and data validations (Hosted on viXra): In addition to the updated framework available on Zenodo, the following earlier publications on this platform represent foundational case studies and data validations for the model’s development:

  1. Star Distance Validation from Data of a High-Z Supernova Ia in the Special Relativity Context
  2. Concerning the Apparent Magnitude
  3. Concerning the Time Dilation of the Supernovae
  4. On the Inaugural Observations of the James Webb Space Telescope: A Short Study of the Stephan’s Quintet

While the papers on apparent magnitude and supernovae time dilation lay the necessary theoretical foundations, the study of a High-Z Supernova Ia serves as a crucial empirical validation of the model’s ability to accurately calculate cosmological distances [1]. Complementing this, the examination of Stephan’s Quintet is not intended as a new astrophysical analysis of the system, but rather as a focused illustration of how the framework’s formulas operate in practice. In this way, the 4 Sphere model is shown to successfully account for the groundbreaking inaugural observations of the James Webb Space Telescope.

[1] ‒ See the section “On the significant validation of the model and more” in A new perspective on Hubble’s law through a four-dimensional spatial model, where the validation of the Type Ia Supernova distance holds a pivotal importance.

Philosophical and Geometric Foundations

Here, the correctness of the FLRW model is not in question; however, it is built upon specific foundational assumptions. My work does not dispute its internal consistency, but explores the consequences of relaxing one of these assumptions, while preserving the Big Bang scenario. Within this modified framework, an alternative cosmological model naturally emerges.

This model is fundamentally simple, rooted in the geometry of the 3-sphere. It belongs to the field of alternative cosmology, though the core concept of the hypersphere has an illustrious origin, being attributed to Einstein himself.

From a macroscopic perspective, the model relies on the physical laws and principles that we apply to the real world; from a microscopic viewpoint, it considers only the particles currently known to the Standard Model. I have termed it the ‘4-Sphere’ model. This choice was made partly to distinguish it from other mathematical treatments, but also because, while setting up a stellar map for the model, I encountered 2D, 3D, and 4D geometric figures intricately intertwined. In that moment, I realized that the mathematical term 3-sphere—though technically correct for the spatial boundary—did not fully capture the profound 4-dimensional spatial reality of the object I was observing.