Running vacuum and H^4-inflation

Abstract

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: $\Lambda =\Lambda (H)$. This running is inherited from the cosmic evolution of the vacuum energy density (VED), ${\rho }_{\mathrm{vac}}$, 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: ${\rho }_{\mathrm{vac}}={\rho }_{\mathrm{vac}}(H,\dot{H},\ddot{H},...)$. Two nearby points of the cosmic evolution during the FLRW epoch are smoothly related as $\delta {\rho }_{\mathrm{vac}}\sim \mathcal{O}(H^2)$. 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 vacuum, which we compute. Herein we focus on the lowest possible power for inflation to occur: $H^4$. 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.

Version accepted in Universe. Typos corrected, extended discussion and references added

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