The concordance Formula: see textCDM model, based on a rigid Formula: see text-term for the entire cosmic history, has been in crisis for a long time. In our expanding Universe, an evolving Formula: see text 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 spacetime, quantum effects induce a vacuum energy density (VED) Formula: see text which is a function of the Hubble rate Formula: see text and its time derivatives, Formula: see text. Currently, Formula: see text evolves very slowly with the expansion, Formula: see text, and this fact provides a possible fundamental origin of dark energy (DE), conceived as dynamical vacuum energy. The RVM framework leads to a “renormalized Formula: see textCDM”, an upgraded version of the concordance model which can help cure the cosmological tensions. In it, Formula: see text is also evolving, but much slower (logarithmically with Formula: see text): Formula: see text. In the very early universe, on the other hand, the vacuum fluctuations of the quantized matter fields induce higher (even) powers, e.g. Formula: see text, capable of triggering fast inflation in a very short period, in which Formula: see text 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 Formula: see text is never constant. Furthermore, the dynamics of Formula: see text and Formula: see text 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 dark energy 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 Formula: see text term.
Joan Sola Peracaula (Fri,) studied this question.