Inverse scale factor in isotropic quantum geometry

By M. Bojowald. 2001

189 citations recorded by the source corpus.

The inverse scale factor, which in classical cosmological models diverges at the singularity, is quantized in isotropic models of loop quantum cosmology by using techniques which have been developed in quantum geometry for a quantization of general relativity. This procedure results in a bounded operator which is diagonalizable simultaneously with the volume operator and whose eigenvalues are determined explicitly. For large scale factors (in fact, up to a scale factor slightly above the Planck length) the eigenvalues are close to the classical expectation, whereas below the Planck length there are large deviations leading to a non-diverging behavior of the inverse scale factor even though the scale factor has vanishing eigenvalues. This is a first indication that the classical singularity is better behaved in loop quantum cosmology.

Subfields: Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/58a1e43a347021a9903e1f423a4b8c18e311999a

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Quantization ambiguities in isotropic quantum geometry (2002, methodology): “However, as in [15] we can use the techniques developed in [8] to quantize the inverse volume; in fact this has already been done for matter Hamiltonians in [13] where the first step is to replace (det q)− 1 2 by det(ea) (2)(det q)− 3 2 .”
Loop quantum cosmology: a status report (2011, unknown): “[38–44]).”
Quantum geometry and the Schwarzschild singularity (2005, background): “This work was supported in part by NSF grants PHY-0090091, PHY-0354932 and PHY0456931, the Alexander von Humboldt Foundation, the C V Raman Chair of the Indian Academy of Sciences and the Eberly research funds of Penn State.”
Introduction to Loop Quantum Cosmology (2011, background): “In fact, from the explicit calculations of inversevolume operators and their spectra in exactly isotropic models and for regular lattice states in the presence of inhomogeneities [41, 52, 66], correction functions implementing inverse-volume corrections approach the classical value always from above”
Spherically symmetric quantum geometry: Hamiltonian constraint (2005, methodology): “The first and most direct one was the modification of matter Hamiltonians at small volume [54, 55], which makes classically diverging energy densities finite along effective trajectories and also played a role for the removal of cosmological singularities.”
Loop Quantum Cosmology (2005, background): “is not only a densely defined operator but even bounded, which one can easily read off from the eigenvalues [41]”
Disappearance of the black hole singularity in loop quantum gravity (2004, background): “A remarkable result of loop quantum cosmology [2] is the disappearance of the initial cosmological singularity present in the classical theory.”
Anomaly freedom in perturbative loop quantum gravity (2008, background): “Otherwise the equations may show the wrong type and number of degrees of freedom if formerly gauge quantities acquire gauge invariant meaning.”
Mathematical structure of loop quantum cosmology (2003, background): “This comes about because, as a detailed examination shows, the minimally coupled matter Hamiltonians annihilate ψ(φ, μ) for μ = 0 [1,25] and Vμo = V−μo .”
Isotropic loop quantum cosmology (2002, methodology): “An extension of the volume operator to gauge non-invariant states is done by using the relation [ΛI , V̂ ] = 0 which follows from gauge invariance of the volume [25].”