Vacuum energy and cosmological constant in QFT in curved spacetime

TL;DR

This paper discusses the running vacuum model (RVM), a quantum field theory-based approach that treats the cosmological constant as a dynamic quantity, potentially resolving key issues in cosmology like the cosmological constant problem and tensions in observational data.

Contribution

It introduces the RVM framework, showing how vacuum energy density varies with the Hubble parameter and its derivatives, offering a unified approach to inflation, dark energy, and the cosmological constant problem.

Findings

RVM predicts vacuum energy density varies as H^2 in the current universe.

Higher order effects in RVM can drive inflationary dynamics.

RVM can alleviate tensions in H_0 and σ_8 measurements.

Abstract

The cosmological constant term (CC), $\Lambda$, is a pivotal ingredient in the standard model of cosmology or $\Lambda$CDM, but it is a rigid quantity for the entire cosmic history. This is unnatural and inconsistent. Different theoretical and phenomenological conundrums suggest that the $\Lambda$CDM necessitates further theoretical underpinning to cope with modern observations. An interesting approach is the framework of the `running vacuum model' (RVM). It endows $\Lambda$ with cosmic dynamics within a fundamental framework since it is based on QFT. In the RVM, the vacuum energy density (VED) appears as a series of powers of the Hubble function and its derivatives, $\rho_{\rm vac} (H, \dot{H},...)$. In the current universe, $\rho_{\rm vac}$ changes as $\sim H^2$. Higher order effects ${\cal O}(H^4)$, on the other hand, can be responsible for a new mechanism of inflation (RVM-inflation). On the practical side the RVM can alleviate the cosmological tensions on $\sigma_8$ and $H_0$. An intriguing smoking gun signature of the RVM is that its equation of state can mimic quintessence, as recently observed by DESI, so the vacuum can be the sought-for dynamical DE. At a deeper theoretical level, the RVM-renormalized form of the VED can avoid extreme fine tuning related to the well-known cosmological constant problem. Overall, the RVM has the capacity to impinge positively on relevant theoretical and practical aspects of modern cosmology.