Starobinsky-Like Inflation and Running Vacuum in the Context of Supergravity

Abstract

Abstract:We describe the primeval inflationary phase of the early Universe within a quantum field theoretical (QFT) framework that can be viewed as the effective action of vacuum decay in the early times. Interestingly enough, the model accounts for the "graceful exit" of the inflationary phase into the standard radiation regime. The underlying QFT framework considered here is supergravity (SUGRA), more specifically an existing formulation in which the Starobinsky-type inflation (de Sitter background) emerges from the quantum corrections to the effective action after integrating out the gravitino fields in their (dynamically induced) massive phase. We also demonstrate that the structure of the effective action in this model is consistent with the generic idea of re-normalization group (RG) running of the cosmological parameters; specifically, it follows from the corresponding RG equation for the vacuum energy density as a function of the Hubble rate, ρ Λ (H). Overall, our combined approach amounts to a concrete-model realization of inflation triggered by vacuum decay in a fundamental physics context, which, as it turns out, can also be extended for the remaining epochs of the cosmological evolution until the current dark energy era.

Supersymmetry, Cosmological Constant and Inflation: Towards a fundamental cosmic picture via “running vacuum”

“…If we considerκ >> κ, however, for instance of orderκ/κ = O(10 3 − 10 4 )), we find that we are able to satisfy the above constraints for a range of values [21], with gravitino mass and global SUSY breaking scale in the ball-park of GUT scale, and the Starobinsky scale of order M ∼ 10 −5 M Pl , which leads to phenomenologically acceptable inflation in the massive gravitino phase, consistent with the Planck-satellite data [6]. In particular, typical values obtained for the parameters of our conformal SUGRA models satisfy [20,24] …”

“…In particular, as discussed in [24], from Einstein's equations in the context of RV, and in particular the conservation equation (Bianchi identity) of the total stress tensor μT μν = 0, one can deduceρ…”

“…The integrated form (29) of the vacuum energy density and the above considerations, provides an effective description of inflation and the subsequent stages of the FLRW Universe evolution in a smooth way [24,25]. In particular, as discussed in [24], from Einstein's equations in the context of RV, and in particular the conservation equation (Bianchi identity) of the total stress tensor μT μν = 0, one can deduceρ…”

“…Nevertheless, non-trivial conclusions about the evolution of the Universe after the phase transition that describes graceful exit from inflation and a smooth connection (in the sense of an evolution in cosmic time) of this phase with the radiation-dominated and subsequent eras of the Universe till the current epoch, can be made by applying the concept of the "running vacuum" [25] (RV) immediately after the exit from inflation [24]. According to the RV hypothesis [25], the dynamical cosmic evolution ("decay") of the inflationary phase ground state ("vacuum") to the standard radiation regime can be described using a "renormalization-group-like" approach, whereby the time evolution of the vacuum energy density ρ Λ (t) is inherited from its dependence on a characteristic cosmic scale variable μ c = μ c (t).…”

“…In such scenarios, which are compatible with the Planck satellite data [6], the rôle of the inflaton field is played by the scalar mode that describes collectively the effects of scalar-curvature-squared terms that characterise the gravitational sector of the one-loop effective action in the broken SUGRA phase, after integrating out the massive gravitinos. In section 4 we apply [24] the running vacuum concept [25] in the effective field theory at the exit of the Starobinsky inflation, in order to ensure a smooth (in cosmic time) connection of that era with radiation-and matter-dominance eras of the Universe, and subsequently with the current era characterised by a small but dominant cosmological-constant type contribution to the cosmic energy density. Finally, conclusions and outlook are presented in section 5.…”