Testing superstring theories with gravitational waves

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 greater than or similar to 10(9) GeV, the test applies to all models containing at least one scalar with mass less than or similar to 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.