Abstract
Abstract The $N=1$ supersymmetric Born–Infeld theory coupled to $N=1$ supergravity in four spacetime dimensions is studied in the presence of a cosmological term with spontaneous supersymmetry breaking. The consistency is achieved by compensating a negative contribution to the cosmological term from the Born–Infeld theory by a positive contribution originating from the gravitino condensate. This leads to an identification of the Born–Infeld scale with the supersymmetry-breaking scale. The dynamical formation of the gravitino condensate in supergravity is reconsidered and the induced one-loop effective potential is derived. Slow-roll cosmological inflation with the gravitino condensate as the inflaton (near the maximum of the effective potential) is viable against the Planck 2018 data and can lead to the inflationary (Hubble) scale as high as $10^{12}$ GeV. Uplifting the Minkowski vacuum (after inflation) to a de Sitter vacuum (dark energy) is possible by the use of the alternative Fayet–Iliopoulos term. Some major physical consequences of our scenario for reheating are also briefly discussed.
Highlights
The gravitino condensate and the gravitino mass gap in N = 1 supergravity [1] coupled to the Volkov–Akulov field [2] in four spacetime dimensions arise as the one-loop effect due to the quartic gravitino interaction coming from the gravitino contribution to the spacetimetorsion [3,4]
The negative results of the Large Hadron Collider (LHC) searches for copious production of black holes imply that the low-scale gravity models may have to be replaced by high-scale gravity models, whose effective Planck scale M Pl is much higher than the TeV scale but is still under the standard scale MPl, i.e
The gravitino condensate can be considered as a viable candidate for the inflaton in supergravity, when assuming the effective gravity scale to be close to theGUT scale that is close to the SUSY-breaking scale in our approach, with all scales close to 1015 GeV
Summary
In this paper we propose the gravitino condensation as the origin and the mechanism of such cancellation in the supergravity extension of the BI theory with spontaneously broken SUSY. It was found that the deformed (new) BI action cannot have a non-vanishing cosmological constant but can have a spontaneously broken local SUSY with a non-vanishing gravitino mass related to the SUSY-breaking scale MBI. This does not explain, the physical origin of the necessary compensating positive term +MB4I. The AV action is the fermionic fragment of the supersymmetric BI theory coupled to supergravity with the spontaneously broken SUSY at the scale MBI. Accounting of a spin-1/2 photino contribution is beyond the scope of our investigation in this paper
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