Loop quantum cosmology of k=1 FRW models

Abstract

The closed, k=1, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semi-classical at some late time, the big-bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the `difficulties' pointed out by Green and Unruh in the k=1 case do not arise in a more systematic treatment. As in k=0 models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the k=0 case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists.

Typos corrected. To appear in Physical Review D

Cited by in corpus (33)

• A new spinfoam vertex for quantum gravity
• Corrected Entropy-Area Relation and Modified Friedmann Equations
• Loop Quantum Dynamics of the Schwarzschild Interior
• Anti-deSitter universe dynamics in LQC
• Is loop quantization in cosmology unique?
• Phenomenological loop quantum geometry of the Schwarzschild black hole
• Loop quantization of spherically symmetric midi-superspaces
• Quantum bounce and cosmic recall
• Quantum cosmology with big-brake singularity
• The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
• The Einstein static universe in Loop Quantum Cosmology
• Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
• Super-inflation in Loop Quantum Cosmology
• Cosmological vector modes and quantum gravity effects
• Linearized dynamics from the 4-simplex Regge action
• Open FRW model in Loop Quantum Cosmology
• Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
• Exact solutions for Big Bounce in loop quantum cosmology
• Thermal fluctuations in loop cosmology
• Lattice Refining Loop Quantum Cosmology and Inflation
• The flat FRW model in LQC: the self-adjointness
• On the Onset of Inflation in Loop Quantum Cosmology
• Recollapsing quantum cosmologies and the question of entropy
• Fermions in Loop Quantum Cosmology and the Role of Parity
• Graceful exit via polymerization of pre-big bang cosmology
• Loop Quantum Cosmology: Effective theories and oscillating universes
• Canonical wave packets in quantum cosmology
• Holography from loop quantum gravity
• The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology
• Universe from vacuum in loop-string cosmology
• Quantum Space-times: Beyond the Continuum of Minkowski and Einstein
• Singularity Resolution in Isotropic Loop Quantum Cosmology: Recent Developments
• Dark Energy as a Relic of the Vacuum-Energy Cancellation?