Physical time and other conceptual issues of QG on the example of LQC

Abstract

Several conceptual aspects of quantum gravity are studied on the example of the homogeneous isotropic LQC model. In particular: $(i)$ The proper time of the co-moving observers is showed to be a quantum operator {and} a quantum spacetime metric tensor operator is derived. $(ii)$ Solutions of the quantum scalar constraint for two different choices of the lapse function are compared and contrasted. In particular it is shown that in case of model with masless scalar field and cosmological constant $\Lambda$ the physical Hilbert spaces constructed for two choices of lapse are the same for $\Lambda <0$ while they are significantly different for $\Lambda >0$. $(iii)$ The mechanism of the singularity avoidance is analyzed via detailed studies of an energy density operator, whose essential spectrum was shown to be an interval $[0,\rhoc]$, where $\rhoc\approx 0.41ρ_{\Pl}$. $(iv)$ The relation between the kinematical and the physical quantum geometry is discussed on the level of relation between observables.

Revtex4, 19 pages, 1 figure, revised to match the version published in CQG

References in corpus (21)

• Quantum Nature of the Big Bang: Improved dynamics
• Loop quantum cosmology of k=1 FRW models
• Loop quantum cosmology and the k = - 1 RW model
• Black holes in loop quantum gravity: the complete space-time
• Closed FRW model in Loop Quantum Cosmology
• Anti-deSitter universe dynamics in LQC
• Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations
• Loop Quantization of Vacuum Bianchi I Cosmology
• Loop quantization of spherically symmetric midi-superspaces
• Quantum bounce and cosmic recall
• Loop Quantum Cosmology in Bianchi Type I Models: Analytical Investigation
• The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
• Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
• Dynamics of interacting phantom scalar field dark energy in Loop Quantum Cosmology
• Open FRW model in Loop Quantum Cosmology
• Exact solutions for Big Bounce in loop quantum cosmology
• Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
• The flat FRW model in LQC: the self-adjointness
• Singularities in loop quantum cosmology
• Elements of Loop Quantum Cosmology
• The status of Quantum Geometry in the dynamical sector of Loop Quantum Cosmology

Cited by in corpus (1)

• A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology