The cosmological constant and the use of cutoffs

TL;DR

This paper demonstrates that certain zero-point energy contributions to the cosmological constant vanish in perturbation theory when using a specific modification, reducing cutoff sensitivity but not solving the cosmological constant problem.

Contribution

It introduces a little-known modification to perturbation theory that shows zero-point energy contributions vanish with cutoffs, impacting cosmological constant calculations.

Findings

Zero-point energy contributions scale as $\Lambda^4$ but vanish in perturbation theory with the modification.

The modification reduces the sensitivity of the cosmological constant to high energy cutoffs.

It questions some assumptions in supersymmetry and the Asymptotic Safety program.

Abstract

Of the contributions to the cosmological constant, zero-point energy and self energy contributions scale as $\Lambda^4$ where $\Lambda$ 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. This reduces the sensitivity of the cosmological constant to the high energy cutoff significantly, 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.