Holonomy Corrections in the Effective Equations for Scalar Mode Perturbations in Loop Quantum Cosmology

TL;DR

This paper derives effective equations for scalar perturbations in loop quantum cosmology incorporating holonomy corrections, ensuring constraint preservation across all curvature scales for wavelengths above the Planck length.

Contribution

It introduces holonomy-corrected effective equations for scalar modes in loop quantum cosmology that remain valid at all curvature scales and preserve the constraints.

Findings

Effective equations include quantum geometry effects.

Constraints are preserved by the dynamics.

Equations are valid for wavelengths larger than the Planck length.

Abstract

We study the dynamics of the scalar modes of linear perturbations around a flat, homogeneous and isotropic background in loop quantum cosmology. The equations of motion include quantum geometry effects and hold at all curvature scales so long as the wavelengths of the inhomogeneous modes of interest remain larger than the Planck length. These equations are obtained by including holonomy corrections in an effective Hamiltonian and then using the standard variational principle. We show that the effective scalar and diffeomorphism constraints are preserved by the dynamics. We also make some comments regarding potential inverse triad corrections.