https://doi.org/10.1140/epjc/s10052-022-11117-y
Regular Article - Theoretical Physics
Equation of state of the running vacuum
Departament de Física Quàntica i Astrofísica, and Institute of Cosmos Sciences, Universitat de Barcelona, Av. Diagonal 647, 08028, Barcelona, Catalonia, Spain
Received:
2
November
2022
Accepted:
5
December
2022
Published online:
16
December
2022
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: 
. This is because in QFT the quantum scaling of 
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 
. In our approach, what we call the ‘cosmological constant’ 
is just the nearly sustained value of 
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 
(
) triggered inflation during a short period in which 
const, the vacuum EoS is very close to 
. This ceases to be true during the FLRW era, where it adopts the EoS of matter during the relativistic (
) and non-relativistic (
) epochs. Interestingly enough, we find that in the late universe the EoS becomes mildly dynamical and mimics quintessence, 
. It finally asymptotes to 
in the remote future, but in the transit the RV helps alleviating the 
and 
tensions.
© The Author(s) 2022
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