Generating function techniques for loop quantum cosmology

TL;DR

This paper introduces generating function techniques to analytically suppress small-scale oscillations in wave function solutions of loop quantum cosmology models, improving the understanding of initial value problems in these systems.

Contribution

It develops an analytical method using generating functions to control wave function oscillations in anisotropic loop quantum cosmology models, advancing beyond trial-and-error approaches.

Findings

Analytical suppression of oscillations in Bianchi I LRS model

Method applicable to more complex models

Insights into initial value problems for quantum cosmology

Abstract

Loop quantum cosmology leads to a difference equation for the wave function of a universe, which in general has solutions changing rapidly even when the volume changes only slightly. For a semiclassical regime such small-scale oscillations must be suppressed, by choosing the parameters of the solution appropriately. For anisotropic models this is not possible to do numerically by trial and error; instead, it is shown here for the Bianchi I LRS model how this can be done analytically, using generating function techniques. Those techniques can also be applied to more complicated models, and the results gained allow conclusions about initial value problems for other systems.