Running vacuum in the expanding universe: A unified QFT paradigm for inflation and dark energy

Abstract

The concordance ΛCDM model, based on a rigid Λ-term for the entire cosmic history, has been in crisis for a long time. In our expanding Universe, an evolving Λ with the expansion is intuitively much more reasonable, especially if a fundamental theoretical reason can be given for it. In the running vacuum model (RVM) framework, based on quantum field theory (QFT) in curved space–time, quantum effects induce a vacuum energy density (VED) ρvac=Λ∕(8πG) which is a function of the Hubble rate H and its time derivatives, ρvac=ρvac(H,H,H,…). Currently, ρvac evolves very slowly with the expansion, δρvac∼O(mPl2H2), and this fact provides a possible fundamental origin of dark energy (DE), conceived as dynamical vacuum energy. The RVM framework leads to a “renormalized ΛCDM”, an upgraded version of the concordance model which can help cure the cosmological tensions. In it, G is also evolving, but much slower (logarithmically with H): G=G(lnH). In the very early universe, on the other hand, the vacuum fluctuations of the quantized matter fields induce higher (even) powers, e.g. ∼H4, capable of triggering fast inflation in a very short period, in which H is very large and approximately constant. This is the mechanism of “RVM-inflation”. It does not require an “inflaton” field since inflation is brought about by pure QFT effects on the dynamical background. It differs from Starobinsky’s inflation, where H is never constant. Furthermore, the dynamics of ρvac(H) and G(H) can also have implications on the frequently discussed possibility that the fundamental “constants” of Nature can be mildly evolving with the cosmic expansion. Putting things together, a unified QFT framework of DE and inflation ensues as a realistic theory for the description of the universe as a whole on fundamental grounds. In it, dynamical VED is predicted and is much welcomed, since it fits in with current DESI measurements, preferring dynamical DE over a rigid Λ term.