2004/02/16 by José B. Almeida, Jose B. Almeida, Almeida, Jose B.
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Physics (physics.gen-ph) #Relativity and Gravitational Theory #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0402075
Corrected in Eq. 18 and following. Added comparison to Friedman equation. 12 pages
openalex publication_date 2004/02/16 · arxiv created 2004/02/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
One can make the very simple hypothesis that the Universe is the inside of an hypersphere in 4 dimensions, where our 3-dimensional world consists of hypersurfaces at different radii. Based on this assumption it is possible to show that Universe expansion at a rate corresponding to flat comes as a direct geometrical consequence without intervening critical density; any mass density is responsible for opening the Universe and introduces a cosmological constant. Another consequence is the appearance of inertia swirls of expanding matter, which can explain observed velocities around galaxies, again without the intervention of dark matter. When restricted to more everyday situations the model degenerates in what has been called 4-dimensional optics; in the paper this is shown to be equivalent to general relativity in all static isotropic metric situations. In the conclusion some considerations bring the discussion to the realm of 4D wave optics.