We provide a simple transfer function that determines the effect of an early
matter dominated era on the gravitational wave background and show that a large
class of compactifications of superstring theory might be tested by
observations of the gravitational wave background from inflation. For large
enough reheating temperatures > 10^9 \GeV the test applies to all models
containing at least one scalar with mass < 10^{12}\GeV that acquires a large
initial oscillation amplitude after inflation and has only gravitational
interaction strength, i.e., a field with the typical properties of a modulus.Comment: 5 pages 2 figures, v2: changes in presentation, refs revised, matches
version in print in PR