Towards a unified quantum field theory of dark energy and inflation: unstable de Sitter vacuum and running vacuum

Abstract Inflation is a necessary cosmic mechanism to cure basic inconsistencies of the standard model of cosmology. In its absence, we could not understand the observed spatial flatness, the homogeneity and isotropy of the CMB, and yet the origin of structure formation, nor the large amount of entropy today. These problems are usually ‘fixed’ by postulating the existence of a scalar field (the ‘inflaton’). However, other less ad hoc options are actually possible. In the running vacuum model (RVM) framework, the vacuum energy density (VED) is a function of the Hubble rate H and its time derivatives: ρ vac = ρ vac ( H , H ˙ , H ¨ , … ) . In this context, the VED is dynamical (there is no rigid cosmological term Λ ). In the Friedmann–Lemaître–Robertson–Walker (FLRW) epoch, ρ vac evolves very slowly with expansion, as befits the observed Λ ≃ const. behavior. In contrast, in the very early Universe the vacuum fluctuations of the quantized matter fields induce higher powers H N capable of unleashing fast inflation in a short period in which H ≃ const. We call this mechanism ‘RVM-inflation’. It does not require an inflaton field since inflation is brought about by pure quantum field theory (QFT) effects on the dynamical background. It is different from Starobinsky’s inflation, in which H is never constant. In this work, we study a closely related scenario: the decay of the exact de Sitter vacuum into FLRW spacetime, in its radiation epoch, and its impact on the current Universe, and compare it with the RVM. The two QFT calculations are renormalized using an off-shell adiabatic prescription. We find that in both cases inflation is driven by H 4 powers accompanied by subleading contributions of order H 2 that ease a graceful-exit transition into the radiation-dominated epoch, where the FLRW regime starts and ultimately develops a mildly evolving VED in the late Universe: δ ρ vac ∼ O ( m Pl