No Smooth Spacetime in Lorentzian Quantum Cosmology and Trans-Planckian Physics

TL;DR

This paper investigates the impact of trans-Planckian physics on Lorentzian quantum cosmology, showing that modifications to dispersion relations do not resolve the divergence issues in perturbation wave functions.

Contribution

It analyzes how trans-Planckian modifications to dispersion relations affect the divergence problems in Lorentzian quantum cosmology perturbations.

Findings

Trans-Planckian physics does not resolve inverse Gaussian divergence.

Modified dispersion relations do not fix perturbation divergence issues.

Lorentzian quantum cosmology remains problematic with trans-Planckian modifications.

Abstract

In minisuperspace quantum cosmology, the Lorentzian path integral formulations of the no-boundary and tunneling proposals have recently been analyzed. But it has been pointed out that the wave function of linearized perturbations around a homogeneous and isotropic background is of an inverse Gaussian form and thus that their correlation functions are divergent. In this paper, we revisit this issue and consider the problem of perturbations in Lorentzian quantum cosmology by modifying the dispersion relation based on trans-Planckian physics. We consider two modified dispersion relations, the generalized Corley-Jacobson dispersion relation with higher momentum terms and the Unruh dispersion relation with a trans-Planckian mode cut-off, as examples. We show that the inverse Gaussian problem of perturbations in Lorentzian quantum cosmology is hard to overcome with the trans-Planckian physics modifying the dispersion relation at short distances.