No smooth spacetime: Exploring primordial perturbations in Lorentzian quantum cosmology

TL;DR

This paper investigates perturbation issues in Lorentzian quantum cosmology, especially in the context of primordial universe creation and trans-Planckian physics, highlighting persistent challenges and potential Gaussian perturbations under specific conditions.

Contribution

It analyzes perturbation problems in Lorentzian quantum cosmology and examines the impact of modified dispersion relations on these issues, providing new insights into their resolution.

Findings

Most quantum cosmological scenarios have serious perturbation problems.

Perturbations can be Gaussian in certain universe creation scenarios with modified dispersion relations.

Resolving perturbation issues with trans-Planckian physics remains challenging.

Abstract

Recent analysis of quantum cosmology has focused on the Lorentzian path integral formulations of both the no-boundary and tunneling proposals. However, it has been criticized that the wave function for linearized perturbations around a homogeneous and isotropic background leads to an inverse Gaussian distribution. This results in divergent correlation functions and cosmological inconsistencies. In this paper we explore these perturbation problems in Lorentzian quantum cosmology, focusing in particular on the quantum creation of closed, flat, and open universes from no spacetime and the beginning of primordial inflation. We show that most quantum cosmological scenarios have serious perturbation problems. We also study the effects of trans-Planckian physics on quantum cosmology, using the generalized Corley-Jacobson dispersion as a case study of modified dispersion relations. Our findings indicate that resolving perturbation problems in Lorentzian quantum cosmology with modified dispersion relations remains a challenge. However, the perturbations can be Gaussian in the quantum creation of the flat or open universe within the confines of the saddle-point approximation and the generalized Corley-Jacobson dispersion.