Holonomy Corrections in the Effective Equations for Scalar Mode Perturbations in Loop Quantum Cosmology
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.
Cite
@article{arxiv.1108.6265,
title = {Holonomy Corrections in the Effective Equations for Scalar Mode Perturbations in Loop Quantum Cosmology},
author = {Edward Wilson-Ewing},
journal= {arXiv preprint arXiv:1108.6265},
year = {2015}
}
Comments
18 pages. v2: Effective scalar constraint is slightly modified, one equation of motion changes; reference added. v3: one derivation added; several discussions and clarifications added; typo corrected; references added