  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.
