How loopy is the quantum bounce? A heuristic analysis of higher order holonomy corrections in LQC

Abstract

A well-motivated extension of higher order holonomy corrections in loop quantum cosmology (LQC) for the $k=0$ Friedmann-Robertson-Walker model is investigated at the level of heuristic effective dynamics. It reveals that the quantum bounce is generic, regardless of the order of corrections, and the matter density remains finite, bounded from above by an upper bound in the regime of the Planckian density, even if all orders of corrections are included. This observation provides further evidence that the quantum bounce is essentially a consequence of the loopy nature (i.e. intrinsic discreteness) of LQC and LQC is fundamentally different from the Wheeler-DeWitt theory; it also encourages one to construct the quantum theory of LQC with the higher order holonomy corrections, which might be understood as related to the higher $j$ representations in the Hamiltonian operator of loop quantum gravity.

5 pages, 1 figure; more remarks and references added; version to appear in PRD

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Cited by in corpus (15)

• Turning Big Bang into Big Bounce: I. Classical Dynamics
• Loop Quantum Gravity
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Loop quantum cosmology with higher order holonomy corrections
• Anomaly free cosmological perturbations with generalised holonomy correction in loop quantum cosmology
• Loop quantization of spherically symmetric midisuperspaces and loop quantum geometry of the maximally extended Schwarzschild spacetime
• Non-Gaussian features from the inverse volume corrections in loop quantum cosmology
• Application of higher order holonomy corrections to perturbation theory of cosmology
• Cosmological inflation driven by holonomy corrections of loop quantum cosmology
• Gravitational waves with generalized holonomy corrections
• Adiabatic and non-adiabatic perturbations for loop quantum cosmology
• Time Asymmetry of Cosmic Background Evolution in Loop Quantum Cosmology
• New Approach to Evolving Gravitational Waves in Loop Quantum Cosmology
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• Examination of the nature of the Bianchi type cosmological singularities