Cosmological constant in F(R) supergravity

A cosmological constant in the regime of low space-time curvature is calculated in the recently proposed version of F® supergravity with a generic cubic function F. The F® supergravity is the N=1 supersymmetric extension of f® gravity. The cubic model is known to successfully describe a chaotic (slow-roll) inflation in the regime of high space-time curvature. We find that a simple extension of the same model allows a positive cosmological constant in the regime of low space-time curvature. The inflaton superfield in F® supergravity (like inflaton in f® gravity) violates the Strong Energy Condition and thus breaks the restriction of the standard supergravity (with usual matter) that can only have either a negative or vanishing cosmological constant.