Truly Lorentzian quantum cosmology

TL;DR

This paper demonstrates that restricting Lorentzian quantum cosmology path integrals to positive squared scale factors alters expectation values and simplifies singularity avoidance, challenging previous semiclassical assumptions.

Contribution

It introduces a Lorentzian path integral formulation with positive squared scale factors, enabling new insights into causal horizons and quantum fluctuations in cosmology.

Findings

Expectation values are significantly affected by the restriction.

Singularity avoidance is achieved by excluding non-Lorentzian geometries.

Semiclassical saddle point approximation may not always be valid.

Abstract

Quantum cosmology based on Lorentzian path integrals is a promising avenue. However, many previous works allow non-Lorentzian configurations by integrating the squared scale factor over the whole real line. Here we show that restricting the minisuperspace path integral to Lorentzian configurations with positive squared scale factor can significantly change the expectation values. In addition, this enables the study of causal horizons and their quantum fluctuations, and achieves singularity avoidance trivially by excluding singular minisuperspace geometries as non-Lorentzian. The results indicate that semiclassical saddle point approximation is not always valid in truly Lorentzian quantum cosmology. As a consequence, related works on the tunnelling and no-boundary proposals, bouncing cosmology, and the quantum origin of inflation etc. need to be reexamined.