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

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.

19 pages; published version

Topics & keywords

References in corpus (8)

• Master field equations for spherically symmetric gravitational fields beyond general relativity
• Long-lived quasinormal modes, shadows and particle motion in four-dimensional quasi-topological gravity
• Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
• Regular Vaidya solutions of effective gravitational theories
• Big bounce and black bounce in quasi-topological gravity
• Regular black holes from pure gravity in four dimensions
• All $2D$ generalised dilaton theories from $d\ge 4$ gravities
• Scattering of a scalar field in the four-dimensional quasi-topological gravity

Cited by in corpus (1)

• Regular ultracompact objects with anti-de Sitter cores as polymerized vacuum solutions