Gaussian fluctuations in the tunneling probability of a closed universe

TL;DR

This paper derives an analytical expression for the tunneling probability of a closed universe, incorporating Gaussian fluctuations to refine semiclassical nucleation rate estimates.

Contribution

It provides a self-consistent semiclassical calculation of universe nucleation rate including quadratic fluctuations around the instanton.

Findings

Derived an explicit tunneling probability including Gaussian prefactor.

Refined previous nucleation rate estimates with fluctuation analysis.

Performed calculations in a fixed-interval minisuperspace framework.

Abstract

We consider the quantum creation of a closed universe within the Euclidean path-integral formalism. An analytical expression for the tunneling probability is derived, including both the exponential suppression and the exact Gaussian prefactor due to quadratic fluctuations around the instanton. The calculation is performed in a fixed-interval minisuperspace formulation, where the Hamiltonian constraint is imposed at the level of the classical instanton, while the full lapse integration is not included beyond the leading semiclassical approximation. The result provides a transparent and self-consistent semiclassical estimate of the nucleation rate, refining previous analyses with the inclusion of Gaussian fluctuations.