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

TL;DR

This paper explores non-polynomial quasi-topological gravity theories in four dimensions, demonstrating their potential to produce non-singular cosmological models such as bouncing universes and universes emerging from de Sitter phases, without Big Bang singularities.

Contribution

It introduces new non-polynomial quasi-topological gravity models that resolve cosmological singularities and describes three distinct non-singular universe scenarios.

Findings

Existence of non-singular cosmological solutions in these theories.

Identification of scenarios with de Sitter emergence, bouncing behavior, and Minkowski-like origins.

Matter density remains finite and non-super-Planckian in these models.

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.