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.

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

References in corpus (10)

• Loop Quantum Cosmology: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Anomaly freedom in perturbative loop quantum gravity
• Loop quantum gravity corrections to gravitational wave dispersion
• Loop quantum cosmology and inhomogeneities
• Lattice refining loop quantum cosmology, anisotropic models and stability
• Gauge invariant cosmological perturbation equations with corrections from loop quantum gravity
• Cosmological vector modes and quantum gravity effects
• The gravitational wave background from super-inflation in Loop Quantum Cosmology

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