Cosmological vector modes and quantum gravity effects

TL;DR

This paper develops a gauge-invariant framework for vector perturbations in bouncing cosmologies, exploring how quantum gravity effects like loop quantum gravity influence their growth, especially near the bounce phase.

Contribution

It introduces a gauge-invariant Hamiltonian formulation for vector modes and analyzes quantum gravity corrections' impact on their evolution in bouncing models.

Findings

Quantum corrections slightly increase vector mode growth in contraction.

Effects at the bounce can significantly alter vector perturbations.

Vector modes grow during contraction, relevant for bounce dynamics.

Abstract

In contrast to scalar and tensor modes, vector modes of linear perturbations around an expanding Friedmann--Robertson--Walker universe decay. This makes them largely irrelevant for late time cosmology, assuming that all modes started out at a similar magnitude at some early stage. By now, however, bouncing models are frequently considered which exhibit a collapsing phase. Before this phase reaches a minimum size and re-expands, vector modes grow. Such modes are thus relevant for the bounce and may even signal the breakdown of perturbation theory if the growth is too strong. Here, a gauge invariant formulation of vector mode perturbations in Hamiltonian cosmology is presented. This lays out a framework for studying possible canonical quantum gravity effects, such as those of loop quantum gravity, at an effective level. As an explicit example, typical quantum corrections, namely those coming from inverse densitized triad components and holonomies, are shown to increase the growth rate of vector perturbations in the contracting phase, but only slightly. Effects at the bounce of the background geometry can, however, be much stronger.