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arXiv · 2509.11573

Topological Big Bangs: Reflection, Itty-Bitty Blenders, and Eternal Trumpets

Hubert Bray·James Wheeler
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Abstract

We discuss and formalize topological means by which the initial singularity might be mollified, at the level of the spacetime manifold's structure, in classical cosmological models of a homogeneous expanding universe. One construction, dubbed a "reflective" topological big bang, generalizes Schrodinger's elliptic de Sitter space and is built to be compatible with the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) picture of the large-scale universe, only minimally modifying it via some nontrivial topology at an earliest "moment" in the universe's history. We establish a mathematical characterization of the admissible topological structures of reflective topological big bangs, and we discuss implications for a standard concern in cosmology, the horizon problem. We present a nonreflective example that we've christened the Itty-Bitty Blender spacetime: this spacetime and its universal cover, the Eternal Trumpet spacetime, exhibit interesting potential structures of spacetimes avoiding the Hawking and Penrose singularity theorems. While these toy models provide a proof-of-concept picture, several questions remain regarding the capacity to realize these structures under physical energy conditions.

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Hubert Bray, James Wheeler. 2025-09-15. Topological Big Bangs: Reflection, Itty-Bitty Blenders, and Eternal Trumpets. https://doi.org/10.1088/1361-6382%2Fae20eb

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