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arXiv · 2603.17654

Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities

Johanna Borissova·João Magueijo
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Abstract

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.

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Johanna Borissova, João Magueijo. 2026-03-18. Modified Friedmann equations and non-singular cosmologies in $d=4$ non-polynomial quasi-topological gravities. https://doi.org/10.1088/1475-7516%2F2026%2F07%2F045

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