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We derive the complete spectrum of gravitational waves induced by primordialscalar perturbations ranging over all observable wavelengths. Thisscalar-induced contribution can be computed directly from the observed scalarperturbations and general relativity and is, in this sense, independent of thecosmological model for generating the perturbations. The spectrum isscale-invariant on small scales, but has an interesting scale-dependence onlarge and intermediate scales, where scalar-induced gravitational waves do notredshift and are hence enhanced relative to the background density of theUniverse. This contribution to the tensor spectrum is significantly differentin form from the direct model-dependent primordial tensor spectrum and,although small in magnitude, it dominates the primordial signal for somecosmological models. We confirm our analytical results by direct numericalintegration of the equations of motion.Comment: 19 pages, 5 figure

Gravitational wave spectrum induced by primordial scalar perturbations