Casimir energy in a small volume multiply connected static hyperbolic pre-inflationary Universe

TL;DR

This paper numerically investigates the Casimir energy in a small, static, multiply connected hyperbolic universe, specifically using the Weeks manifold, revealing spontaneous vacuum excitations and extending previous flat space calculations.

Contribution

It generalizes previous flat space Casimir energy calculations to hyperbolic universes, providing an exact numerical analysis for the Weeks manifold.

Findings

Spontaneous vacuum excitation of low multipolar components.

Casimir energy calculated for a hyperbolic universe with the Weeks manifold.

Extension of flat space Casimir calculations to curved, multiply connected spaces.

Abstract

A few years ago, Cornish, Spergel and Starkman (CSS), suggested that a multiply connected ``small'' Universe could allow for classical chaotic mixing as a pre-inflationary homogenization process. The smaller the volume, the more important the process. Also, a smaller Universe has a greater probability of being spontaneously created. Previously DeWitt, Hart and Isham (DHI) calculated the Casimir energy for static multiply connected flat space-times. Due to the interest in small volume hyperbolic Universes (e.g. CSS), we generalize the DHI calculation by making a a numerical investigation of the Casimir energy for a conformally coupled, massive scalar field in a static Universe, whose spatial sections are the Weeks manifold, the smallest Universe of negative curvature known. In spite of being a numerical calculation, our result is in fact exact. It is shown that there is spontaneous vacuum excitation of low multipolar components.