Running vacuum in QFT in FLRW spacetime: the dynamics of rho _{textrm{vac}}(H) from the quantized matter fields

Abstract

Phenomenological work in the last few years has provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution and that this running helps to alleviate the cosmological tensions afflicting the Lambda CDM. On the theoretical side, recent devoted studies have shown that the properly renormalized rho _{textrm{vac}} in QFT in FLRW spacetime adopts the ‘running vacuum model’ (RVM) form. While in three previous studies by two of us (CMP and JSP) such computations focused solely on scalar fields non-minimally coupled to gravity, in the present work we compute the spin-1/2 fermionic contributions and combine them both. The calculation is performed using a new version of the adiabatic renormalization procedure based on subtracting the UV divergences at an off-shell renormalization point M. The quantum scaling of rho _{textrm{vac}} with M turns into cosmic evolution with the Hubble rate, H. As a result the ‘cosmological constant’ Lambda appears in our framework as the nearly sustained value of 8pi G(H)rho _{textrm{vac}}(H) around (any) given epoch H, where G(H) is the gravitational coupling, which is also running, although very mildly (logarithmically). We find that the VED evolution at present reads delta rho _textrm{vac}(H)sim nu _{textrm{eff}}, m_{textrm{Pl}}^2 left( H^2-H_0^2 right) (|nu _{textrm{eff}}|ll 1). The coefficient nu _{textrm{eff}} receives contributions from all the quantized fields, bosons and fermions, which we compute here for an arbitrary number of matter fields. Remarkably, there also exist higher powers mathcal{O}(H^{6}) which can trigger inflation in the early universe. Finally, the equation of state (EoS) of the vacuum receives also quantum corrections from bosons and fermion fields, shifting its value from − 1. The striking consequence is that the EoS of the quantum vacuum may nowadays effectively appears as quintessence.