MODULAR COSMOLOGY

We begin a study of the cosmology of moduli in string theory. The quantum field theory requirement of ''naturality'' is shown to be incompatible with slow roll inflationary cosmology unless very stringent constraints are satisfied. In most cases, these constraints imply the existence of fields with the properties of string moduli: their natural range of variation must be the Planck scale. The scale which characterizes their potential energy (the inflation scale) must be two to three orders of magnitude smaller than the Planck mass in order to explain the observed magnitude of the fluctuations in the cosmic microwave background. Even if these constraints are satisfied, generic initial conditions near the Planck energy density do not lead to inflation unless the theory contains topological defects. In this case inflation can arise naturally at the cores of the defects. We show that string theory has two generic types of domain walls which could be the seeds for inflation, and argue that modular physics provides a very robust model of inflation. Two scenarios are presented to explain the discrepancy between the inflation scale and the scale of supersymmetry breaking. One of them is favored because it leads to a natural understanding of why the dilaton does not run out to the weak coupling region in the postinflationary period.