Superconformal symmetry, supergravity and cosmology

Abstract

We introduce the general N = 1 gauge theory superconformallycoupled to supergravity. The theory has local SU(2,2|1) symmetry andno dimensional parameters. The superconformal origin of theFayet-Iliopoulos (FI) terms is clarified. The phase of this theory withspontaneously broken conformal symmetry gives various formulations ofN = 1 supergravity interacting with matter, depending on the choice ofthe R-symmetry fixing.We have found that the locally superconformal theory is usefulfor describing the physics of the early universe with a conformally flatFRW metric. Few applications of superconformal theory to cosmologyinclude the study of (a) particle production after inflation,particularly the nonconformal helicity-±½ states ofgravitino,(b) the super-Higgs effect in cosmology and the derivation ofthe equations for the gravitino interacting with any number of chiral and vector multipletsin the gravitational background with varying scalar fields, (c)the weak-coupling limit of supergravity MP→∞ andgravitino-goldstino equivalence. This explains why gravitino productionin the early universe is not suppressed in the limit of weakgravitational coupling.We discuss the possible existence of anunbroken phase of the superconformal theories, interpreted as a strong-coupling limitof supergravity MP→0.