Equation of state of the running vacuum

TL;DR

This paper explores the equation of state of the running vacuum in cosmology, showing its evolution from early universe inflation to late-time acceleration, and its potential to address current cosmological tensions.

Contribution

It provides a quantum field theory-based calculation of the running vacuum's equation of state across cosmic history, linking vacuum energy to the Hubble rate and its derivatives.

Findings

Vacuum EoS close to -1 during inflation

EoS transitions to matter-like values in FLRW epochs

Late universe EoS mimics quintessence, approaching -1

Abstract

Recent studies of quantum field theory in FLRW spacetime suggest that the cause of the speeding up of the universe is the running vacuum (RV). Appropriate renormalization of the energy-momentum tensor shows that the vacuum energy density is a smooth function of the Hubble rate and its derivatives: $\rho_{\rm vac}=\rho_{\rm vac}(H, \dot{H},\ddot{H},...)$. This is because in QFT the quantum scaling of $\rho_{\rm vac}$ with the renormalization point turns into cosmic evolution with $H$. As a result, any two nearby points of the cosmic expansion during the standard FLRW epoch are smoothly related through $\delta\rho_{\rm vac}\sim {\cal O}(H^2)$. In our approach, what we call the `cosmological constant' $\Lambda$ is just the nearly sustained value of $8\pi G(H)\rho_{\rm vac}(H)$ around (any) given epoch, where $G(H)$ is the running gravitational coupling. In the present study, after summarizing the main QFT calculations supporting the RV approach, we focus on the calculation of the equation of state (EoS) of the RV for the entire cosmic history within such a QFT framework. In particular, in the very early universe, where higher (even) powers $\rho_{\rm vac}\sim{\cal O}(H^N)$ ($N=4,6,\dots$) triggered inflation during a short period in which $H=$const, the vacuum EoS is very close to $w_{\rm vac}=-1$. This ceases to be true during the FLRW era, where it adopts the EoS of matter during the relativistic ($w_{\rm vac}=1/3$) and non-relativistic ($w_{\rm vac}=0$) epochs. Interestingly enough, we find that in the late universe the EoS becomes mildly dynamical and mimics quintessence, $w_{\rm vac}\gtrsim-1$. It finally asymptotes to $-1$ in the remote future, but in the transit the RV helps alleviating the $H_0$ and $\sigma_8$ tensions.