Affine ANEC selects the closed FRW branch for geodesically complete cosmology
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918510153695232 |
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| author | Burwig, Nathan L. Easson, Damien A. |
| author_facet | Burwig, Nathan L. Easson, Damien A. |
| contents | We study the relation between geodesic completeness, the averaged null energy condition (ANEC), and spatial curvature in Friedmann--Robertson--Walker (FRW) cosmology within classical general relativity. Using the affinely parameterized ANEC along radial null geodesics, we prove that non-static flat or open FRW spacetimes in the regular classes considered here cannot be both null geodesically complete and ANEC-satisfying. Bounded oscillatory or cyclic flat/open models do not circumvent the obstruction: the negative affine-ANEC bulk term accumulates over infinitely many cycles, giving \(I_{\rm ANEC}=-\infty\) for non-static periodic cases. Equivalently, within these classes, non-static ANEC-satisfying flat or open models are null incomplete. The sign obstruction is absent in closed \((k=+1)\) FRW geometry, where the positive curvature term enters the affine ANEC identity with the opposite sign and can support nonsingular, geodesically complete cosmologies with ordinary NEC-respecting matter. We give explicit closed-FRW scalar-field constructions, including a fully analytic quadratic reconstruction and a cubic-root reconstruction in closed quadrature, and contrast them with their flat realizations, which require NEC-violating support. Furthermore, we quantify how positive curvature can bias flat-model reconstructions toward an effective phantom equation of state, finding only a percent-level effect under current curvature bounds. The result is a curvature classification of ANEC-compatible eternal FRW cosmology: flat and open branches are obstructed, while the closed branch admits explicit complete realizations, with global de Sitter appearing as the vacuum limiting representative. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_18965 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Affine ANEC selects the closed FRW branch for geodesically complete cosmology Burwig, Nathan L. Easson, Damien A. General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory We study the relation between geodesic completeness, the averaged null energy condition (ANEC), and spatial curvature in Friedmann--Robertson--Walker (FRW) cosmology within classical general relativity. Using the affinely parameterized ANEC along radial null geodesics, we prove that non-static flat or open FRW spacetimes in the regular classes considered here cannot be both null geodesically complete and ANEC-satisfying. Bounded oscillatory or cyclic flat/open models do not circumvent the obstruction: the negative affine-ANEC bulk term accumulates over infinitely many cycles, giving \(I_{\rm ANEC}=-\infty\) for non-static periodic cases. Equivalently, within these classes, non-static ANEC-satisfying flat or open models are null incomplete. The sign obstruction is absent in closed \((k=+1)\) FRW geometry, where the positive curvature term enters the affine ANEC identity with the opposite sign and can support nonsingular, geodesically complete cosmologies with ordinary NEC-respecting matter. We give explicit closed-FRW scalar-field constructions, including a fully analytic quadratic reconstruction and a cubic-root reconstruction in closed quadrature, and contrast them with their flat realizations, which require NEC-violating support. Furthermore, we quantify how positive curvature can bias flat-model reconstructions toward an effective phantom equation of state, finding only a percent-level effect under current curvature bounds. The result is a curvature classification of ANEC-compatible eternal FRW cosmology: flat and open branches are obstructed, while the closed branch admits explicit complete realizations, with global de Sitter appearing as the vacuum limiting representative. |
| title | Affine ANEC selects the closed FRW branch for geodesically complete cosmology |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.18965 |