The Vertex Expansion in the Consistent Histories Formulation of Spin Foam Loop Quantum Cosmology

TL;DR

This paper extends the consistent histories approach in loop quantum cosmology to a covariant spin foam framework, demonstrating that the probability of a non-singular bounce in the universe is unity.

Contribution

It provides a covariant generalization of previous results by expressing loop quantum cosmology within the spin foam paradigm and calculating transition amplitudes via vertex expansion.

Findings

Probability of a non-singular bounce is unity.

Spin foam formulation successfully generalizes consistent histories results.

Supports the robustness of bounce predictions in quantum cosmology.

Abstract

Assignment of consistent quantum probabilities to events in a quantum universe is a fundamental challenge which every quantum cosmology/gravity framework must overcome. In loop quantum cosmology, this issue leads to a fundamental question: What is the probability that the universe undergoes a non-singular bounce? Using the consistent histories formulation, this question was successfully answered recently by the authors for a spatially flat FRW model in the canonical approach. In this manuscript, we obtain a covariant generalization of this result. Our analysis is based on expressing loop quantum cosmology in the spin foam paradigm and using histories defined via volume transitions to compute the amplitudes of transitions obtained using a vertex expansion. We show that the probability for bounce turns out to be unity.