Revisiting semiclassical effective dynamics for quantum cosmology

TL;DR

This paper refines the semiclassical effective dynamics technique in quantum cosmology, providing more efficient formulas for Poisson brackets and applying them to isotropic models, including noncompact spacetimes.

Contribution

It introduces a systematic, simplified algorithm for evaluating Poisson structures in semiclassical quantum cosmology, improving computational efficiency and applicability.

Findings

Derived closed-form Poisson brackets with fewer summations.

Applied formulas to isotropic cosmological models with matter fields.

Established a consistent limit for noncompact spacetimes.

Abstract

We revise the technique of semiclassical effective dynamics, in particular reexamining the evaluation of Poisson structure of the so-called central moments capturing quantum corrections, providing a systematic, pedagogical, and efficient algorithm for evaluation of said structure. The resulting closed formulae for Poisson brackets involve less summatios than recent results in the literature, thus being more optimal for applications. Found formulae are then applied to a general class of isotropic cosmological models with locally observable configuration variables for the admitted matter fields. In particular, this allowed to formulate a consistent and nontrivial limit or fiducial cell (infrared regulator) removal for models describing spatially noncompact spacetimes.