Compactification and inflation in the superstring theory from the condensation of gravitino pairs

We discuss the possibility that inflation can occur in the E₈×E₈′ heterotic superstring theory, if there is a pair condensation of the gravitino field ψ_A and also of the Majorana-Weyl spinor λ, as suggested by the Helayël-Neto and Smith. In the absence of a condensation of the anti-symmetric tensor field H_MNP, then the associated potential V(θ,φ) is bounded from below and independent of the dilaton field φ. It can be made to vanish at the minimum, where the compactification scale θ is fixed. Alternatively, a small cosmological constant may remain (ultimately to be cancelled by radiative corrections at the lower energy scale of the gaugino condensation), which could in principle lead to inflation.