Cosmological constant and the use of cutoffs

Abstract

Of the contributions to the cosmological constant, zero-point energy contributions scale as ${\ensuremath{\delta}}^{4}(0)\ensuremath{\sim}{\mathrm{\ensuremath{\Lambda}}}^{4}$ where $\mathrm{\ensuremath{\Lambda}}$ is an ultraviolet cutoff used to regulate the calculations. I show that such contributions vanish when calculated in perturbation theory. This demonstration uses a little-known modification to perturbation theory found by Honerkamp and Meetz and by Gerstein, Jackiw, Lee, and Weinberg which comes into play when using cutoffs and interactions with multiple derivatives, as found in chiral theories and gravity. In a path integral treatment, the new interaction arises from the path integral measure and cancels the ${\ensuremath{\delta}}^{4}(0)$ contributions. This reduces the sensitivity of the cosmological constant to the high energy cutoff, although it does not resolve the cosmological constant problem. The feature removes one of the common motivations for supersymmetry. It also calls into question some of the results of the asymptotic safety program. Covariance and quadratic cutoff dependence are also briefly discussed.