COSMOLOGICAL MODULI PROBLEM, SUPERSYMMETRY BREAKING, AND STABILITY INPOSTINFLATIONARY COSMOLOGY

We review scenarios that have been proposed to solve the cosmological problem caused by moduli in string theory, the postmodern Polonyi prob lem (PPP). In particular, we discuss the difficulties encountered by t he apparently ''trivial'' solution of this problem, in which moduli ma sses are assumed to arise from nonperturbative, SUSY-preserving, dynam ics at a scale higher than that of SUSY breaking. This suggests a powe rful cosmological vacuum selection principle in superstring theory. Ho wever, we argue that if one eschews the possibility of cancellations b etween different exponentials of the inverse string coupling, the mech anism described above cannot stabilize the dilaton. Thus, even if supe rsymmetric dynamics gives mass to the other moduli in string theory, t he dilaton mass must be generated by SUSY breaking, and dilaton domina tion of the energy density of the Universe cannot be avoided. We concl ude that the only proposal for solving the PPP that works is the inter mediate scale inflation scenario of Randall and Thomas. However, we po int out that all extent models have ignored unavoidably large inhomoge neities in the cosmological moduli density at very early times, and sp eculate that the effects associated with nonlinear gravitational colla pse of these inhomogeneities may serve as an efficient mechanism for c onverting moduli into ordinary matter. As an important by-product of t his investigation we show that in a postinflationary universe minima o f the effective potential with a negative cosmological constant are no t stationary points of the classical equations of scalar field cosmolo gy Instead, such points lead to catastrophic gravitational collapse of that part of the Universe which is attracted to them. Thus postinflat ionary cosmology dynamically chooses non-negative values of the cosmol ogical constant. This implies that supersymmetry must be broken in any sensible inflationary cosmology. We suggest that further study of the cosmology of moduli will lead to additional important insight about c osmology, SUSY breaking, and the choice of the vacuum in superstring t heory.