Anomaly free cosmological perturbations with generalised holonomy correction in loop quantum cosmology

TL;DR

This paper explores a generalized holonomy correction in loop quantum cosmology, deriving anomaly-free perturbation equations and analyzing inflationary power spectra, extending the standard $ar{ ext{μ}}$ scheme.

Contribution

It introduces a generalized function for holonomy correction, fixes counter terms for anomaly freedom, and derives gauge-invariant perturbation equations in this new framework.

Findings

Derived anomaly-free gauge-invariant perturbation equations.

Identified restrictions on the form of the generalized holonomy function.

Analyzed inflationary power spectra with the new correction scheme.

Abstract

In the spatially flat case of loop quantum cosmology, the connection $\bar{k}$ is usually replaced by the holonomy $\frac{\sin(\bar{\mu}k)}{\bar{\mu}}$ in the effective theory. In this paper, instead of the $\bar{\mu}$ scheme, we use a generalised, undertermined function $g(\bar{k},\bar{p})$ to represent the holonomy and by using the approach of anomaly free constraint algebra we fix all the counter terms in the constraints and find the restriction on the form of $g(\bar{k},\bar{p})$, then we derive the gauge invariant equations of motion of the scalar, tensor and vector perturbations and study the inflationary power spectra with generalised holonomy correction.