Casimir energy in a small volume multiply connected static hyperbolic pre-inflationary Universe
arXiv:gr-qc/0103014 · doi:10.1103/PhysRevD.63.123508
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.
accepted for publication in phys. rev. D
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