Casimir energy in a small volume multiply connected static hyperbolic preinflationary universe

Abstract

A few years ago, Cornish, Spergel and Starkman ͑CSS͒ suggested that a multiply connected ''small'' universe could allow for classical chaotic mixing as a preinflationary 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 ͑DHI͒ calculated the Casimir energy for static multiply connected flat space-times. Because of the interest in small volume hyperbolic universes ͑e.g., CSS͒, we generalize the DHI calculation by making 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.

News and Views: Challenges of Relativistic Astrophysics

“…Dewitt, Hart and Isham (50) calculated the Casimir energy for static multiply connected flat space-times. A generalization of this calculation was made by us in (42,43), showing that there is a spontaneous vacuum excitation of low multipolar components.…”

“…Initially the Universe was very small and thus its Casimir energy was very large. We calculated the spatial distribution of the Casimir energy in the primordial Universe (42,43). Cornish, Spergel and Starkman (49) suggested yhat a multiply connected "small" universe could allow for classical chaotic mixing as a preinflationary homogenization process.…”

Casimir Energy Density in Closed Hyperbolic Universes

“…To avoid this one replaces x by x ′ in the first factor, then in the second factor, and average the result. Thus the above expectation value becomes one-half Hadamard's function G (1) :…”

“…Here we develop a formalism succintly described in [1], for the numerical calculation of the CE density of closed hyperbolic universes. …”

“…In a previous work [1] the Casimir energy density was obtained for a RobertsonWalker (RW) cosmological model with constant, negative spatial curvature.…”