Alternative $k=-1$ loop quantum cosmology

Abstract

An alternative quantization of the gravitational Hamiltonian constraint of the $k=-1$ Friedmann-Robertson-Walker model is proposed by treating the Euclidean term and the Lorentzian term independently, mimicking the treatment of full loop quantum gravity. The resulting Hamiltonian constraint operator for the $k=-1$ model with a massless scalar field is successfully constructed, and is shown to have the corrected classical limit. Compared to the former quantization schemes in the literature where only the Euclidean term is quantized, the new quantum dynamics of the $k=-1$ model with a massless scalar field indicates that the classical big-bang singularity is replaced by an asymmetric quantum bounce.

10 pages, 3 figures; V2, 15 pages, 3 figures, version published in PRD

References in corpus (13)

• Quantum Nature of the Big Bang: Improved dynamics
• Loop quantum cosmology of k=1 FRW models
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Loop Quantum Cosmology: An Overview
• Loop quantum cosmology and the k = - 1 RW model
• Closed FRW model in Loop Quantum Cosmology
• Extension of loop quantum gravity to $f(R)$ theories
• Open FRW model in Loop Quantum Cosmology
• New length operator for loop quantum gravity
• Effective Dynamics from Coherent State Path Integral of Full Loop Quantum Gravity
• Effective Scenario of Loop Quantum Cosmology
• Bouncing evolution in a model of loop quantum gravity
• Loop quantum cosmology and the Wheeler-De Witt equation

Cited by in corpus (4)

• Loop quantum black hole
• Quantum Oppenheimer-Snyder models in loop quantum cosmology with Lorentz term
• Effective Dynamics of Loop Quantum Kaluza-Klein Cosmology
• Unitary evolution and cosmic acceleration in Loop Quantum Cosmology