Affine quantization and the initial cosmological singularity

Abstract

The Affine Coherent State Quantization procedure is applied to the case of a FRLW universe in the presence of a cosmological constant. The quantum corrections alter the dynamics of the system in the semiclassical regime, providing a potential barrier term which avoids all classical singularities, as already suggested in other models studied in the literature. Furthermore the quantum corrections are responsible for an accelerated cosmic expansion. This work intends to explore some of the implications of the recently proposed "Enhanced Quantization" procedure in a simplified model of cosmology.

A new rule for quantization that resolves all problems

“…These include covariant scalar fields [7,8,9,10,11], and quantum gravity [7,12,13,14]. The use of special variables to discuss idealized cosmological models [15,16] has led to gravitational bounces rather than an initial singularity of the universe. Further use of special variables as applied to idealized gravitational models has been given in various papers, e.g., [17,18,19], and references therein.…”

Quantum field theory with no zero-point energy

“…Enhanced quantization and affine variables have also been applied to other problems. The use of affine variables to discuss idealized cosmological models [8,9] has led to gravitational bounces rather than an initial singularity of the universe. Further use of affine variables applied to idealized gravitational models has been given in seveal papers, e.g., [10,11,12], and references therein.…”

Towards the Quantum Geometry of Saturated Quantum Uncertainty Relations: The Case of the (Q, P) Heisenberg Observables

“…When combined with the normalisation factor in (119), the Gaussian integration in (123) leads to a factor which may be brought into the form of this last factor (cosh r) −1/2 being multiplied by a specific phase factor. In order to express the thereby determined phase factor ϕ(z, 0), let us introduce two last angular parametersθ ± (z) defined by, 14 Since one has the relations i…”

“…Correspondingly the saturating quantum states are the so-called and well known general squeezed states, for which many properties and results were reviewed and presented together with quite many details and some original results, with the hope that some readers could become interested in taking part in such an exploration in the case of other possible choices of quantum observables and the ensuing saturating quantum states. For instance, the affine quantum algebra of scale transformations, [Q, D] = i Q (say with D = (QP + P Q)/2), does also play an important role in quite many quantum systems [4,6,7,14], with its own coherent states. To this author's best knowledge, the analogue states for the affine algebra of the squeezed states for the Heisenberg algebra remain to be fully understood.…”