On the possible running of the cosmological "constant"

TL;DR

This paper explores the potential for the cosmological constant to have a mild running behavior due to quantum effects in curved spacetime, which could explain dark energy's dynamical nature.

Contribution

It revisits the fundamental aspects of the cosmological constant in Quantum Field Theory, proposing the possibility of its running and emphasizing the need for deeper understanding of vacuum contributions.

Findings

No definitive proof of the cosmological constant running exists.

Quantum effects could induce a mild running of the CC in curved spacetime.

Understanding vacuum contributions of massive quantum fields is crucial.

Abstract

Despite the many outstanding cosmological observations leading to a strong evidence for a nonvanishing cosmological constant (CC) term in the gravitational field equations, the theoretical status of this quantity seems to be lagging well behind the observational successes. It thus seems timely to revisit some fundamental aspects of the CC term in Quantum Field Theory (QFT). We emphasize that, in curved space-time, nothing a priori prevents this term from potentially having a mild running behavior associated to quantum effects. Remarkably, this could be the very origin of the dynamical nature of the Dark Energy, in contrast to many other popular options considered in the literature. In discussing this possibility, we also address some recent criticisms concerning the possibility of such running. Our conclusion is that, while there is no comprehensive proof of the CC running, there is no proof of the non-running either. The problem can be solved only through a deeper understanding of the vacuum contributions of massive quantum fields on a curved spacetime background. We suggest that such investigations are at the heart of one of the most important endeavors of fundamental theoretical cosmology in the years to come.