Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity

TL;DR

This paper derives gauge-invariant cosmological perturbation equations incorporating loop quantum gravity corrections, revealing impacts on early universe inhomogeneities, power conservation, and non-adiabaticity, emphasizing the importance of consistent gauge treatment.

Contribution

It provides the first consistent derivation of gauge-invariant perturbation equations with inverse triad corrections from loop quantum gravity, highlighting the necessity of inhomogeneous metric modes.

Findings

Power conservation on large scales may be affected.

Non-adiabatic effects can arise due to quantum corrections.

Consistency conditions constrain quantization ambiguities.

Abstract

A consistent implementation of quantum gravity is expected to change the familiar notions of space, time and the propagation of matter in drastic ways. This will have consequences on very small scales, but also gives rise to correction terms in evolution equations of modes relevant for observations. In particular, the evolution of inhomogeneities in the very early universe should be affected. In this paper consistent evolution equations for gauge-invariant perturbations in the presence of inverse triad corrections of loop quantum gravity are derived. Some immediate effects are pointed out, for instance concerning conservation of power on large scales and non-adiabaticity. It is also emphasized that several critical corrections can only be seen to arise in a fully consistent treatment where the gauge freedom of canonical gravity is not fixed before implementing quantum corrections. In particular, metric modes must be allowed to be inhomogeneous: it is not consistent to assume only matter inhomogeneities on a quantum corrected homogeneous background geometry. In this way, stringent consistency conditions arise for possible quantization ambiguities which will eventually be further constrained observationally.