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A new supergravity D-term, not associated to gauged R-symmetry, was recentlydiscovered and used to construct new supergravity models. In this paper we usea generalization of the new D-term that we used in previous works, to constructa supergravity model of slow-roll inflation with the observable sector of theminimal supersymmetric standard model. Supersymmetry is broken at a high scalein the hidden sector and communicated to the observable sector by gravitymediation. The new D-term contains free parameters that can give large massesto scalar superpartners of quarks and leptons and to the higgsinos whileholding the masses of observed particles fixed. Gauginos receive a mass from anon-canonical kinetic term for the vector supermultiplets. We also present asimple argument proving in full generality that the cutoff $\Lambda$ ofeffective theories containing new D-terms can never exceed the supersymmetrybreaking scale. In our theory, the relation between D-term and the Hubbleconstant during inflation also implies the universal relation $\Lambda \lesssim\sqrt{H M_{Pl}}$.

A Realization of Slow Roll Inflation and the MSSM in Supergravity Theories with New Fayet-Iliopoulos Terms