Superconformal symmetry, supergravity and cosmology

We introduce the general N = 1 gauge theory superconformally coupled to sup ergravity. The theory has local SU(2, 2\1) symmetry and no dimensional para meters. The superconformal origin of the Fayet-Iliopoulos (FI) terms is cla rified. The phase of this theory with spontaneously broken conformal symmet ry gives various formulations of N = 1 supergravity interacting with matter , depending on the choice of the R-symmetry fixing. We have found that the locally superconformal theory is useful for describi ng the physics of the early universe with a conformally flat FRW metric. Fe w applications of superconformal theory to cosmology include the study of ( a) particle production after inflation, particularly the nonconformal helic ity-/-1.2 sates of gravitino, (b) the super-Higgs effect in cosmology and t he derivation of the equations for the gravitino interacting with any numbe r of chiral and Vector multiplets in the gravitational background with vary ing scalar fields, (c) the weak-coupling limit of supergravity Mp --> infin ity and gravitino-goldstino equivalence. This explains why gravitino produc tion in the early universe is not suppressed in the limit of weak gravitati onal coupling. We discuss the possible existence of an unbroken phase of the superconforma l theories, interpreted as a strong-coupling limit of supergravity Mp --> 0 .