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Measuring the primordial power spectrum on small scales is a powerful tool ininflation model building, yet constraints from Cosmic Microwave Backgroundmeasurements alone are insufficient to place bounds stringent enough to beappreciably effective. For the very small scale spectrum, those which subtendangles of less than 0.3 degrees on the sky, an upper bound can be extractedfrom the astrophysical constraints on the possible production of primordialblack holes in the early universe. A recently discovered observationalby-product of an enhanced power spectrum on small scales, induced gravitationalwaves, have been shown to be within the range of proposed space basedgravitational wave detectors; such as NASA's LISA and BBO detectors, and theJapanese DECIGO detector. In this paper we explore the impact such a detectionwould have on models of inflation known to lead to an enhanced power spectrumon small scales, namely the Hilltop-type and running mass models. We find thatthe Hilltop-type model can produce observable induced gravitational waveswithin the range of BBO and DECIGO for integral and fractional powers of thepotential within a reasonable number of e-folds. We also find that the runningmass model can produce a spectrum within the range of these detectors, butrequire that inflation terminates after an unreasonably small number ofe-folds. Finally, we argue that if the thermal history of the Universe were toaccomodate such a small number of e-folds the Running Mass Model can producePrimordial Black Holes within a mass range compatible with Dark Matter, i.e.within a mass range 10^{20}g< M_{BH}<10^{27}g.

Observable Spectra of Induced Gravitational Waves from Inflation