Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities
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| Format: | Preprint |
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2026
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| _version_ | 1866914406015696896 |
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| author | Borissova, Johanna Magueijo, João |
| author_facet | Borissova, Johanna Magueijo, João |
| contents | Quasi-topological theories of gravity are known to resolve black-hole singularities. We investigate whether the same mechanism can remove cosmological singularities. Focusing on non-polynomial curvature quasi-topological gravities in $d=4$ dimensions, we find three generic scenarios with the correct infrared limit but without a Big-Bang singularity, for universes filled with pure radiation or other standard matter. The first scenario yields a universe emerging from a de Sitter phase, a case for which the curvature invariants remain finite but the matter density diverges, albeit only at infinite affine distance. The second one corresponds to a bouncing universe, which requires a multi-valued Lagrangian. The third possibility is an asymptotically Minkowski origin, reminiscent of an eternally loitering universe. The matter energy density for this solution is non-singular even at infinite affine distance and does not enter a super-Planckian regime, but is instead approximately constant for the past eternity. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_17654 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities Borissova, Johanna Magueijo, João General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics Quasi-topological theories of gravity are known to resolve black-hole singularities. We investigate whether the same mechanism can remove cosmological singularities. Focusing on non-polynomial curvature quasi-topological gravities in $d=4$ dimensions, we find three generic scenarios with the correct infrared limit but without a Big-Bang singularity, for universes filled with pure radiation or other standard matter. The first scenario yields a universe emerging from a de Sitter phase, a case for which the curvature invariants remain finite but the matter density diverges, albeit only at infinite affine distance. The second one corresponds to a bouncing universe, which requires a multi-valued Lagrangian. The third possibility is an asymptotically Minkowski origin, reminiscent of an eternally loitering universe. The matter energy density for this solution is non-singular even at infinite affine distance and does not enter a super-Planckian regime, but is instead approximately constant for the past eternity. |
| title | Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics |
| url | https://arxiv.org/abs/2603.17654 |