Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect

TL;DR

This paper explores how zeta regularization can be used to calculate the vacuum energy contributions from boundary conditions and topology in quantum field theory, with implications for cosmological constant estimates.

Contribution

It demonstrates the application of zeta regularization to boundary conditions and topology in higher-dimensional models, providing finite vacuum energy estimates relevant to cosmology.

Findings

The incremental vacuum energy can match observed cosmological constant scales.

Boundary conditions and topology significantly influence vacuum energy calculations.

Models with compactified scales and brane boundary conditions yield realistic energy contributions.

Abstract

Zeta regularization has proven to be a powerful and reliable tool for the regularization of the vacuum energy density in ideal situations. With the Hadamard complement, it has been shown to provide finite (and meaningful) answers too in more involved cases, as when imposing physical boundary conditions (BCs) in two-- and higher--dimensional surfaces (being able to mimic, in a very convenient way, other {\it ad hoc} cut-offs, as non-zero depths). What we have considered is the {\it additional} contribution to the cc coming from the non-trivial topology of space or from specific boundary conditions imposed on braneworld models (kind of cosmological Casimir effects). Assuming someone will be able to prove (some day) that the ground value of the cc is zero, as many had suspected until very recently, we will then be left with this incremental value coming from the topology or BCs. We show that this value can have the correct order of magnitude in a number of quite reasonable models involving small and large compactified scales and/or brane BCs, and supergravitons.