Application of higher order holonomy corrections to perturbation theory of cosmology

TL;DR

This paper investigates higher order holonomy corrections in cosmological perturbation theory within Loop Quantum Cosmology, revealing a revised parameter range, anomaly-free conditions, and quantum-induced gravitational wave mass.

Contribution

It introduces a new analysis of the lattice power law parameter range and derives anomaly-free conditions for vector and tensor modes in loop quantum cosmology.

Findings

Revised range for the lattice power law parameter: [-1, 0]

Existence of anomaly-free conditions in the theory

Quantum effects induce a nonzero mass for gravitational waves

Abstract

Applying the higher order holonomy corrections to the perturbation theory of cosmology, the lattice power law of Loop Quantum Cosmology, $\tilde{\mu}\propto p^{\beta}$, is analysed and the range of $\beta$ is decided to be [-1,0] which is different from the conventional range $-0.1319>\beta\geq-5/2$ \cite{lqct}. At the same time, we find that there is a anomaly free condition in this theory, and we obtain this condition in the vector and tensor mode. We also find that the nonzero mass of gravitational wave essentially results from the quantum nature of Riemannian geometry of loop quantum gravity.