Vacuum energy and spectral function sum rules

TL;DR

This paper explores how spectral function sum rules can explain the cancellation of vacuum energy divergences, with applications to Minkowski and de Sitter spaces, impacting cosmological models.

Contribution

It reformulates vacuum energy divergence cancellation using spectral function sum rules and applies this framework to different space-time geometries.

Findings

Spectral sum rules can enforce vacuum energy cancellation.

Application to Minkowski and de Sitter spaces demonstrates the approach.

Conditions on the fundamental spectrum are derived.

Abstract

We reformulate the problem of the cancellation of the ultraviolet divergencies of the vacuum energy, particularly important at the cosmological level, in terms of a saturation of spectral function sum rules which leads to a set of conditions on the spectrum of the fundamental theory. We specialize the approach to both Minkowski and de Sitter space-times and investigate some examples.