Running Vacuum and H4 Inflation

Recent studies of QFT in cosmological spacetime indicate that the speeding up of the present universe may not just be associated with a rigid cosmological term but with a running one that evolves with the expansion rate Λ=Λ(H). This running is inherited from the cosmic evolution of the vacuum energy density (VED), ρvac, which is sensitive to quantum effects in curved spacetime that ultimately trigger that running. The VED is a function of the Hubble rate and its time derivatives ρvac=ρvac(H,H˙,H¨,…). Two nearby points of cosmic evolution during the FLRW epoch are smoothly related as δρvac∼O(H2). In the very early universe, in contrast, the higher powers of the Hubble rate take over and bring about a period of fast inflation. They originate from quantum effects on the effective action of a vacuum, which we compute. Herein, we focus on the lowest possible power for inflation to occur: H4. During the inflationary phase, H remains approximately constant and very large. Subsequently, the universe enters the usual FLRW radiation epoch. This new mechanism (‘RVM inflation’) is not based on any supplementary ‘inflaton’ field; it is fueled by pure QFT effects on the dynamical background and is different from Starobinsky’s inflation, in which H is never constant.