The Cosmological Constant Problem and Running Vacuum in the Expanding Universe

TL;DR

This paper explores a running vacuum model where the vacuum energy density evolves mildly with the universe's expansion rate, potentially addressing the cosmological constant problem and observational tensions in cosmology.

Contribution

It proposes a quantum field theory-based framework for a dynamical vacuum energy that naturally avoids fine-tuning issues and can alleviate current cosmological tensions.

Findings

The vacuum energy density acquires an ${\cal O}(H^2)$ dynamical component.

The model can mimic quintessence without new fields.

It may help resolve the $H_0$ and $\sigma_8$ tensions.

Abstract

It is well-known that quantum field theory (QFT) induces a huge value of the cosmological constant, $\Lambda$, which is outrageously inconsistent with cosmological observations. We review here some aspects of this fundamental theoretical conundrum (`the cosmological constant problem') and strongly argue in favor of the possibility that the cosmic vacuum density $\rho_{\rm vac}$ may be mildly evolving with the expansion rate $H$. Such a `running vacuum model' (RVM) proposal predicts an effective dynamical dark energy without postulating new ad hoc fields (quintessence and the like). Using the method of adiabatic renormalization within QFT in curved spacetime we find that $\rho_{\rm vac}(H)$ acquires a dynamical component ${\cal O}(H^2)$ caused by the quantum matter effects. There are also ${\cal O}(H^n)$ ($n=4,6,..$) contributions, some of which may trigger inflation in the early universe. Remarkably, the evolution of the adiabatically renormalized $\rho_{\rm vac}(H)$ is not affected by dangerous terms proportional to the quartic power of the masses ($\sim m^4$) of the fields. Traditionally, these terms have been the main source of trouble as they are responsible for the extreme fine tuning feature of the cosmological constant problem. In the context under study, however, the late time $\rho_{\rm vac}(H)$ around $H_0$ is given by a dominant term ($\rho_{\rm vac}^0$) plus the aforementioned mild dynamical component $\propto \nu (H^2-H_0^2)$ (with $|\nu|\ll1$), which makes the RVM to mimic quintessence. Finally, on the phenomenological side we show that the RVM may be instrumental in alleviating some of the most challenging problems (so-called `tensions') afflicting nowadays the observational consistency of the `concordance' $\Lambda$CDM model, such as the $H_0$ and $\sigma_8$ tensions.