Topological Regularization of the Inverse Cosmological Problem: Perelman's Theorem in Black Hole Bounce Scenarios
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2026
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| _version_ | 1866901749314355200 |
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| author | Petrov, Sergey |
| author_facet | Petrov, Sergey |
| contents | <p>Reconstructing global properties of the Universe from cosmological observations is generically an<br>ill-posed inverse problem, primarily due to unresolved degeneracies in spatial topology. Distinct<br>topological classes may produce observationally indistinguishable signatures within a finite observable<br>volume. We demonstrate that this degeneracy can be eliminated under a physically motivated<br>scenario in which the Universe originates from a nonsingular bounce inside a parent black hole described<br>by Einstein–Cartan gravity. Horizon formation and causal disconnection imply that spatial<br>hypersurfaces are compact and simply connected.</p> <p>Under these assumptions, Perelman’s proof of the Geometrization Conjecture enforces a unique<br>topological class, allowing the admissible spatial topology to be restricted to the three-sphere. We<br>formulate this result as a delta-function Bayesian prior over topology, acting as an exact topological<br>regularizer with vanishing entropy.</p> <p>This construction restores well-posedness of the cosmological inverse problem in the<br>topological sector, under explicit physical assumptions. It allows observational data to constrain<br>only physical parameters, such as curvature radius and anisotropy, without contamination<br>from spurious topological degrees of freedom. We discuss how this framework enables consistent<br>Bayesian inference from cosmic microwave background measurements and stochastic gravitationalwave<br>observations. The role of geometrization is thus clarified: Perelman’s theorem uniquely<br>determines the admissible diffeomorphism class of spatial hypersurfaces once compactness<br>and simple connectedness are assumed, guaranteeing the internal consistency of<br>cosmological inference.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18140929 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Topological Regularization of the Inverse Cosmological Problem: Perelman's Theorem in Black Hole Bounce Scenarios Petrov, Sergey Cosmology Einstein-Cartan Gravity Black Hole Bounce Topology Perelman Theorem Inverse Problem Bayesian Inference <p>Reconstructing global properties of the Universe from cosmological observations is generically an<br>ill-posed inverse problem, primarily due to unresolved degeneracies in spatial topology. Distinct<br>topological classes may produce observationally indistinguishable signatures within a finite observable<br>volume. We demonstrate that this degeneracy can be eliminated under a physically motivated<br>scenario in which the Universe originates from a nonsingular bounce inside a parent black hole described<br>by Einstein–Cartan gravity. Horizon formation and causal disconnection imply that spatial<br>hypersurfaces are compact and simply connected.</p> <p>Under these assumptions, Perelman’s proof of the Geometrization Conjecture enforces a unique<br>topological class, allowing the admissible spatial topology to be restricted to the three-sphere. We<br>formulate this result as a delta-function Bayesian prior over topology, acting as an exact topological<br>regularizer with vanishing entropy.</p> <p>This construction restores well-posedness of the cosmological inverse problem in the<br>topological sector, under explicit physical assumptions. It allows observational data to constrain<br>only physical parameters, such as curvature radius and anisotropy, without contamination<br>from spurious topological degrees of freedom. We discuss how this framework enables consistent<br>Bayesian inference from cosmic microwave background measurements and stochastic gravitationalwave<br>observations. The role of geometrization is thus clarified: Perelman’s theorem uniquely<br>determines the admissible diffeomorphism class of spatial hypersurfaces once compactness<br>and simple connectedness are assumed, guaranteeing the internal consistency of<br>cosmological inference.</p> |
| title | Topological Regularization of the Inverse Cosmological Problem: Perelman's Theorem in Black Hole Bounce Scenarios |
| topic | Cosmology Einstein-Cartan Gravity Black Hole Bounce Topology Perelman Theorem Inverse Problem Bayesian Inference |
| url | https://doi.org/10.5281/zenodo.18140929 |