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

Johanna Borissova, João Magueijo

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.

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 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.
Paper Structure (8 sections, 59 equations, 4 figures)

This paper contains 8 sections, 59 equations, 4 figures.

Table of Contents

  1. Introduction
  2. 2D Horndeski theory for FLRW cosmologies
  3. Conditions for acceleration
  4. Non-singular FLRW cosmologies
  5. de Sitter asymptotic universe
  6. Bouncing universe
  7. Minkowski asymptotic universe
  8. Conclusions

Figures (4)

  • Figure 1: Examples of choices of characteristic functions $h\qty(H^2)$ resulting in Big-Bang singularity resolution via an asymptotic de Sitter phase, a bounce, or an asymptotic Minkowski phase.
  • Figure 2: Scale factor as a function of time for a $d=4$ radiation-dominated FLRW universe with characteristic function $h$ in \ref{['eq:hdeSitter']} according to \ref{['eq:adeSitter']}. The curve shows a transition from exponential expansion at early times to a power-law scaling at late times.
  • Figure 3: Scale factor as a function of time for a $d=4$ radiation-dominated FLRW universe with characteristic function $h$ in \ref{['eq:hBounce']} according to \ref{['eq:aBounce']}. The curve shows a bounce at $\tau =0$ where $\dot{a}(0)=0$ and a power-law scaling at early and late times.
  • Figure 4: Scale factor as a function of time for a $d=4$ radiation-dominated FLRW universe with characteristic function $h$ given by the inverse of \ref{['eq:hMinkInv']} according to \ref{['eq:aMinkowski']}. The curve shows a transition from a finite constant scale factor at early times to a power-law scaling at late times.