  We derive the complete spectrum of gravitational waves induced by primordial
scalar perturbations ranging over all observable wavelengths. This
scalar-induced contribution can be computed directly from the observed scalar
perturbations and general relativity and is, in this sense, independent of the
cosmological model for generating the perturbations. The spectrum is
scale-invariant on small scales, but has an interesting scale-dependence on
large and intermediate scales, where scalar-induced gravitational waves do not
redshift and are hence enhanced relative to the background density of the
Universe. This contribution to the tensor spectrum is significantly different
in form from the direct model-dependent primordial tensor spectrum and,
although small in magnitude, it dominates the primordial signal for some
cosmological models. We confirm our analytical results by direct numerical
integration of the equations of motion.
