Lorentzian quantum cosmology from effective spin foams

TL;DR

This paper demonstrates the first effective spin foam calculations of Lorentzian quantum cosmology, specifically for a de Sitter universe, highlighting the impact of discrete spectra and advanced summation techniques.

Contribution

It introduces a novel computational approach for Lorentzian quantum cosmology using effective spin foams, including techniques to handle oscillatory sums.

Findings

Successful computation of a finite time evolution in Lorentzian de Sitter universe

Identification of high order Shanks transformation as an effective summation method

Insights into effects of discrete area spectra in spin foam models

Abstract

Effective spin foams provide the computationally most efficient spin foam models yet and are therefore ideally suited for applications e.g. to quantum cosmology. We provide here the first effective spin foam computations of a finite time evolution step in a Lorentzian quantum de Sitter universe. We will consider a set-up which computes the no-boundary wave function, as well as a set-up describing the transition between two finite scale factors. A key property of spin foams is that they implement discrete spectra for the areas. We therefore study the effects that are induced by the discrete spectra. To perform these computations we had to identify a technique to deal with highly oscillating and slowly converging, or even diverging sums. We illustrate here that high order Shanks transformation work very well and are a promising tool for the evaluation of Lorentzian (gravitational) path integrals and spin foam sums.