| _version_ | 1866901900967804928 |
|---|---|
| author | Peacock, Samuel Hall, Lauren |
| author_facet | Peacock, Samuel Hall, Lauren |
| contents | <p>Inverted Hypersphere Cosmology (IHC) posits that the universe is the real projective four-space RP4 = S4/Z2, derived from a single non-preferential axiom with zero free parameters. This topology has three immediate consequences for singularity physics. First, the Hartle-Hawking no-boundary condition follows directly from the axiom rather than being imposed as an extra postulate: the pre-geometric vacuum selects compact boundaryless Euclidean 4-geometries, so no initial singular boundary exists. Second, the antipodal identification on S4 is precisely CPT symmetry on de Sitter spacetime; every black hole at position x is therefore CPT-paired with a white hole at its antipodal partner -x, approximately 14 Gpc distant. The singularity at x is identified with its CPT image, becoming a traversable junction: geodesics extend through it with total affine parameter delta-lambda = 2.24M (finite), while the Kretschmann scalar K = 48M2/r6 still diverges. Third, the non-trivial fundamental group pi1(RP4) = Z2 prevents a global Cauchy surface, rendering the Penrose singularity theorem inapplicable in its standard form. Information is conserved nonlocally through the antipodal pairing on timescale t ~ pi*R_S/c ~ 44 Gyr.</p> <p>Two observational tests are presented. Against the Planck 2018 low-l CMB spectrum, the IHC Hartle-Hawking infrared cutoff at k_min = H0/c reduces the quadrupole tension from -4.77 sigma (LCDM) to -0.69 sigma, with delta-chi2 = 26.6 over l = 2-3. An MCMC fit over l = 2-29 independently recovers the RP4-corrected cutoff scale 2H0/c at 0.02 sigma from the posterior median, with Hamimeche-Lewis delta-ln-L = +2.71 against LCDM. The Z2 projection (even-l bosonic modes only) is confirmed at the sub-0.1 sigma level. Against GWTC-4.0 (44 confident binary black hole events from O1-O4a), IHC predicts local dynamics identical to general relativity (gamma_PPN = 1), achieving chi2/n = 0.110 with the Hawking area theorem satisfied in all 44 events with 29-36% margin. The joint Bayes factor across independent datasets is ln B = +11.07 (odds 64,216:1, decisive evidence on the Jeffreys scale).</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20070971 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Singularity Absence and Black Hole Information Resolution in Inverted Hypersphere Cosmology Peacock, Samuel Hall, Lauren inverted hypersphere cosmology singularity resolution black hole information paradox Hartle-Hawking no-boundary RP4 topology CMB quadrupole suppression GWTC-4 Penrose theorem CPT symmetry antipodal identification Bayes factor gravitational waves cosmological constant dark energy <p>Inverted Hypersphere Cosmology (IHC) posits that the universe is the real projective four-space RP4 = S4/Z2, derived from a single non-preferential axiom with zero free parameters. This topology has three immediate consequences for singularity physics. First, the Hartle-Hawking no-boundary condition follows directly from the axiom rather than being imposed as an extra postulate: the pre-geometric vacuum selects compact boundaryless Euclidean 4-geometries, so no initial singular boundary exists. Second, the antipodal identification on S4 is precisely CPT symmetry on de Sitter spacetime; every black hole at position x is therefore CPT-paired with a white hole at its antipodal partner -x, approximately 14 Gpc distant. The singularity at x is identified with its CPT image, becoming a traversable junction: geodesics extend through it with total affine parameter delta-lambda = 2.24M (finite), while the Kretschmann scalar K = 48M2/r6 still diverges. Third, the non-trivial fundamental group pi1(RP4) = Z2 prevents a global Cauchy surface, rendering the Penrose singularity theorem inapplicable in its standard form. Information is conserved nonlocally through the antipodal pairing on timescale t ~ pi*R_S/c ~ 44 Gyr.</p> <p>Two observational tests are presented. Against the Planck 2018 low-l CMB spectrum, the IHC Hartle-Hawking infrared cutoff at k_min = H0/c reduces the quadrupole tension from -4.77 sigma (LCDM) to -0.69 sigma, with delta-chi2 = 26.6 over l = 2-3. An MCMC fit over l = 2-29 independently recovers the RP4-corrected cutoff scale 2H0/c at 0.02 sigma from the posterior median, with Hamimeche-Lewis delta-ln-L = +2.71 against LCDM. The Z2 projection (even-l bosonic modes only) is confirmed at the sub-0.1 sigma level. Against GWTC-4.0 (44 confident binary black hole events from O1-O4a), IHC predicts local dynamics identical to general relativity (gamma_PPN = 1), achieving chi2/n = 0.110 with the Hawking area theorem satisfied in all 44 events with 29-36% margin. The joint Bayes factor across independent datasets is ln B = +11.07 (odds 64,216:1, decisive evidence on the Jeffreys scale).</p> |
| title | Singularity Absence and Black Hole Information Resolution in Inverted Hypersphere Cosmology |
| topic | inverted hypersphere cosmology singularity resolution black hole information paradox Hartle-Hawking no-boundary RP4 topology CMB quadrupole suppression GWTC-4 Penrose theorem CPT symmetry antipodal identification Bayes factor gravitational waves cosmological constant dark energy |
| url | https://doi.org/10.5281/zenodo.20070971 |