The Wave Function of the Universe by the New Euclidean Path-integral Approach in Quantum Cosmology

TL;DR

This paper introduces a new regularization method for the Euclidean path integral to compute the wave function of the universe, addressing divergence issues and applying it to minisuperspace models in quantum cosmology.

Contribution

A novel regularization technique for Euclidean path integrals is proposed, enabling finite wave function calculations for cosmological models.

Findings

Successfully regularized the Euclidean path integral for minisuperspace models.

Computed the wave function for Friedmann-Robertson-Walker and Bianchi type I models.

Analyzed the physical interpretation of the wave function with the new method.

Abstract

The wave function of the universe is evaluated by using the Euclidean path integral approach. As is well known, the real Euclidean path integral diverges because the Einstein-Hilbert action is not positive definite. In order to obtain a finite wave function, we propose a new regularization method and calculate the wave function of the Friedmann- Robertson-Walker type minisuperspace model. We then consider a homogeneous but anisotropic type minisuperspace model, which is known as the Bianch type I model. The physical meaning of the wave function by this new regularization method is also examined.