We discuss the gravitational wave background generated by primordial density perturbations evolving during the radiation era. At second order in a perturbative expansion, density fluctuations produce gravitational waves. We calculate the power spectra of gravitational waves from this mechanism, and show that, in principle, future gravitational wave detectors could be used to constrain the primordial power spectrum on scales vastly different from those currently being probed by a large-scale structure. As examples we compute the gravitational wave background generated by both a power-law spectrum on all scales, and a delta-function power spectrum on a single scale.

• Received 13 March 2007

DOI:https://doi.org/10.1103/PhysRevD.75.123518