Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects

TL;DR

This paper analyzes the structure and utility of spin foam-like expansions in loop quantum cosmology, highlighting their strengths for conceptual and quantum-scale questions and limitations for large-scale cosmological dynamics.

Contribution

It provides a detailed examination of the properties of the vertex expansion in spin foam loop quantum cosmology and discusses its applicability and limitations.

Findings

Expansion is useful for conceptual and quantum-scale analysis.

High-order expansion needed for cosmological scale dynamics.

Finite truncation of expansion is potentially uncontrolled.

Abstract

We explore the structure of the spin foam-like vertex expansion in loop quantum cosmology and discuss properties of the corresponding amplitudes, with the aim of elucidating some of the expansion's useful properties and features. We find that the expansion is best suited for consideration of conceptual questions and for investigating short-time, highly quantum behavior. In order to study dynamics at cosmological scales, the expansion must be carried to very high order, limiting its direct utility as a calculational tool for such questions. Conversely, it is unclear that the expansion can be truncated at finite order in a controlled manner.