Equation of state of the running vacuum

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), see Moreno-Pulido and Solà Peracaula (Eur Phys J C 82(6):551, 2022; Eur Phys J C 80(8):692, 2020). 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 _textrm{vac}=rho _textrm{vac}(H, {dot{H}},ddot{H},ldots ). This is because in QFT the quantum scaling of rho _textrm{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 _textrm{vac}sim mathcal{O}(H^2). In our approach, what we call the ‘cosmological constant’ Lambda is just the nearly sustained value of 8pi G(H)rho _textrm{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 _textrm{vac}sim mathcal{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_textrm{vac}=-1. This ceases to be true during the FLRW era, where it adopts the EoS of matter during the relativistic (w_textrm{vac}=1/3) and non-relativistic (w_textrm{vac}=0) epochs. Interestingly enough, we find that in the late universe the EoS becomes mildly dynamical and mimics quintessence, w_textrm{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.