Vacuum energy and spectral function sum rules
  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. 
A. Y. Kamenshchik, A. Tronconi, G. P. Vacca and G. Venturi