Quantum vacuum energy in Taub-NUT (Newman-Unti-Tamburino)-type cosmologies

Abstract

The effects of vacuum polarization on the mildest possible sort of cosmological singularity, the Taub-NUT (Newman-Unti-Tamburino)-type singularities, are studied. Unlike stronger sorts of singularities where physical quantities (e.g., curvature, energy density) diverge, in these universes the only barrier is a pathological topology. Quantum effects, known to be important in regions of large spacetime curvature, are found to also be important in these universes, where the curvature may be arbitrarily small or even zero. The vacuum expectation value of the stress-energy tensor for a conformal scalar field is calculated on a flat archetype of the Taub-NUT-type universes, the Misner universe (flat Kasner spacetime with ${S}^{1}\ifmmode\times\else\texttimes\fi{}{R}^{3}$ topology). The vacuum stress energy diverges at the singularity and on its associated Cauchy horizons. This divergence, together with the "fixed" nature of the spacetime's topology, suggests that these boundaries will be replaced by curvature singularities in a better approximation to full quantum gravity.