Aspects of the Running Vacuum Model in Quantum Field Theory

Abstract

The measured non-zero value of a Cosmological Constant (CC), Λ, has been the source of many theoretical discussions at the core of the concordance ΛCDM. The identification of the value of Λ/(8πG) in the gravitational action with the vacuum energy density (VED) leads to a huge discrepancy between theory and observations, due to ∼ m4 contributions (for any quantum field with mass m) and forces an absurd fine-tuning of the parameters. Running Vacuum Models (RVM), characterized by a dependence of the VED with even powers of the Hubble rate, offer a possible solution to this fine-tuning problem. Phenomenologically, even though the ΛCDM model has been an observational triumph for some time, precision measurements of CMB, BAO, SNIa, LSS and other sources currently threaten its validity because of tensions around the observational values of H0 and σ8. In this context, the RVM proposal predicts an evolving behaviour that might help alleviate these tensions. The aim of this work is to expose how the method of adiabatic renormalization in curved spacetime applied to a quantized scalar field non-minimally coupled to gravity reproduces the dynamical VED of the RVM, ρvac(H). We find how in the recent universe this VED deviates from the CC through a mild component ∼ νH2, with |ν| ≪ 1, accompanied with a logarithmic running of the gravitational coupling G(lnH). We also study the impact of quantum effects in the equation of state of the vacuum, which is no longer wvac = −1. Finally, we verify how the higher order O(H4) contributions may be responsible for a genuinely new mechanism of inflation in the early universe, called RVM-inflation