  We discuss a novel mechanism to generate gravitational waves in the early
universe. A standard way to produce primordial black holes is to enhance at
small-scales the overdensity perturbations generated during inflation. The
latter, upon horizon re-entry, collapse into black holes. They must be sizeable
enough and are therefore associated to rare peaks. There are however less
sizeable and much less rare overdensity peaks which do not end up forming
primordial black holes and have a non-spherical shape. Upon collapse, they
possess a time-dependent non-vanishing mass quadrupole which gives rise to the
generation of gravitational waves. By their nature, such gravitational waves
are complementary to those sourced at second-order by the very same scalar
perturbations responsible for the formation of the primordial black holes.
Their amplitude is nevertheless typically about two orders of magnitude smaller
and therefore hardly measurable.
