The secondary spectra of the gravitons induced by a waterfall-like field are computed and the general bounds on the spectral energy density of the tensor modes of the geometry are translated into explicit constraints on the amplitude and slope of the waterfall spectrum. The obtained results are compared with the primary gravitational wave spectra of the concordance model and of its neighboring extensions as well as with the direct LIGO/Virgo bounds on stochastic backgrounds of relic gravitons. Space-borne interferometers [such as LISA (Laser Interferometer Space Antenna), BBO (Big Bang Observer), and DECIGO (Deci-hertz Interferometer Gravitational Wave Observatory)] seem to be less relevant but their potential implications are briefly outlined.

• Received 6 August 2010

DOI:https://doi.org/10.1103/PhysRevD.82.083523