The Cosmological Moduli Problem, Supersymme- Try Breaking , and Stability in Postinflationary Cos- Mology

We review scenarios that have been proposed to solve the cosmological problem caused by moduli in string theory, the Postmodern Polonyi Problem (PPP). In particular, we discuss the difficulties encountered by the apparently " trivial " solution of this problem, in which moduli masses are assumed to arise from nonperturbative, SUSY preserving, dynamics at a scale higher than that of SUSY breaking. This suggests a powerful cosmological vacuum selection principle in superstring theory. However, we argue that if one eschews the possibility of cancellations between different exponentials of the inverse string coupling, the mechanism described above cannot stabilize the dilaton. Thus, even if supersymmetric dynamics gives mass to the other moduli in string theory, the dilaton mass must be generated by SUSY breaking, and dilaton domination of the energy density of the universe cannot be avoided. We conclude that the only proposal for solving the PPP that works is the intermediate scale inflation scenario of Randall and Thomas. However, we point out that all extant models have ignored unavoidably large inhomogeneities in the cosmological moduli density at very early times, and speculate that the effects associated with nonlinear gravitational collapse of these inhomogeneities may serve as an efficient mechanism for converting moduli into ordinary matter. As an important byproduct of this investigation, we show that in a postinflationary universe, minima of the effective potential with negative cosmological constant are not stationary points of the classical equations of scalar field cosmology. Instead, such points lead to catastrophic gravitational collapse of that part of the universe which is attracted to them. Thus postinflationary cosmology dynamically chooses nonnegative values of the cosmological 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 insights about cosmology, SUSY breaking, and the choice of the vacuum in superstring theory.