2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/206617We 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.11 pages, revtex4, no figures, version to be published on PRDHigh Energy Physics - TheoryGeneral Relativity and Quantum CosmologyHigh Energy Physics - Phenomenologytext