Vacuum energy and the topology of the universe

Abstract

We analyze the dependence of the quantum vacuum energy on the space topology. In particular we point out the existence of a renormalization ambiguity in spaces with non-vanishing curvature. The ambiguity is related to the well known ambiguity of the R2 term of the gravitational effective action. However, there are two extra universal contributions which are genuine dependent on the topological structure of the space and completely independent of the renormalization scheme. The ambiguity does not appear in flat spaces where only the topological dependent contributions are non-vanishing. We analyze the cosmological role of universal contributions to the vacuum energy and its attractive nature in the case of conformal scalar fields.