Cosmic gravitational-wave background in a cyclic universe

Inflation predicts a primordial gravitational wave spectrum that is slightly ``red.'' In this Brief Report, we compute both the amplitude and spectral form of the primordial tensor spectrum predicted by cyclic or ekpyrotic models under the assumption that perturbations pass smoothly through the bounce. The spectrum is exponentially suppressed compared to inflation on long wavelengths. The strongest constraint is that the energy density in gravitational waves is less than 10% of the critical density at nucleosynthesis.