text: Galaxies and their dark matter haloes form from small density perturbations in the expanding Universe. These overdense regions expand more slowly than the rest of the Universe and eventually "turn around" – start collapsing instead of expanding. The blue dots in this figure (for a standard LCDM reference model) show that at this turnaround epoch, these galaxy formation regions are positively curved. If the Universe were flat, galaxies could not be formed. Roukema & Ostrowski 2019, JCAP 12, 049 [arXiv:1902.09064], https://codeberg.org/boud/1902.09064
text: How can Newtonian gravitation, the limit of Einstein's gravity, be extended to non-Euclidean topologies? A proposed minimal reasonable extension is Non-Euclidean Newtonian (NEN) theory. In any spherical topology, the gravitational potential created at distance ξ (in radians) from a massive point object of mass M at a given epoch is given by the formula above instead of the Euclidean-space Newtonian formula - GM/ξ, where A is a constant that depends on the topology of the universe being studied. At small distances it approaches the flat-Euclidean case; and at the antipode, it approaches zero, avoiding the paradox of requiring a negative mass object. Vigneron & Roukema 2022, PRD 107, 063545 [arXiv:2201.09102], https://codeberg.org/boud/topoaccel