Can the cosmological "constant" run? - It may run

TL;DR

This paper explores the theoretical possibility of the cosmological constant running with energy scale, emphasizing its relevance for dark energy models and addressing recent criticisms against this idea.

Contribution

It provides a pedagogical review of the theoretical debate on the running of the cosmological constant, challenging claims that deny its possibility.

Findings

No comprehensive proof of CC running exists

Counterarguments to non-running theorems are unsubstantiated

The possibility of CC running remains open and theoretically plausible

Abstract

Using standard quantum field theory, we discuss several theoretical aspects of the possible running of the cosmological constant (CC) term in Einstein's equations. The basic motivation for the present work is to emphasize that this possibility should also be taken into account when considering dynamical models for the dark energy (DE), which are nowadays mainly focused on identifying the DE with the energy density associated to one or more ad hoc scalar fields. At the same time, we address some recent criticisms that have been published (or privately communicated to us) attempting to cast doubts on the fundamental possibility of such running. In this work, we argue that while there is no comprehensive proof of the CC running, there is no rigorous proof of the non-running either. In particular, some purported "non-running theorem" recently adduced in the literature is, in our opinion, completely insubstantial and formally incorrect. The way to the CC running is, therefore, still open and we take here the opportunity to present a pedagogical review of the present state of the art in this field, including a a brief historical account.