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.

5 pages 2 figures, v2: changes in presentation, refs revised, matches version in print in PRD