  Gravitational waves are inevitably produced by second order terms in
cosmological perturbation theory. Most notably, the so-called induced
gravitational waves are a window to the small scales part of the primordial
spectrum of fluctuations and a key counterpart to the primordial black hole
scenario. However, semi-analytical solutions are only known for matter and
radiation domination eras. In this paper, we present new analytic integral
formulas for the induced gravitational waves on subhorizon scales in a general
cosmological background with a constant equation of state. We also discuss
applications to a peaked primordial scalar power spectrum and the primordial
black hole scenario.
