Observable Spectra of Induced Gravitational Waves from Inflation
  Measuring the primordial power spectrum on small scales is a powerful tool in
inflation model building, yet constraints from Cosmic Microwave Background
measurements alone are insufficient to place bounds stringent enough to be
appreciably effective. For the very small scale spectrum, those which subtend
angles of less than 0.3 degrees on the sky, an upper bound can be extracted
from the astrophysical constraints on the possible production of primordial
black holes in the early universe. A recently discovered observational
by-product of an enhanced power spectrum on small scales, induced gravitational
waves, have been shown to be within the range of proposed space based
gravitational wave detectors; such as NASA's LISA and BBO detectors, and the
Japanese DECIGO detector. In this paper we explore the impact such a detection
would have on models of inflation known to lead to an enhanced power spectrum
on small scales, namely the Hilltop-type and running mass models. We find that
the Hilltop-type model can produce observable induced gravitational waves
within the range of BBO and DECIGO for integral and fractional powers of the
potential within a reasonable number of e-folds. We also find that the running
mass model can produce a spectrum within the range of these detectors, but
require that inflation terminates after an unreasonably small number of
e-folds. Finally, we argue that if the thermal history of the Universe were to
accomodate such a small number of e-folds the Running Mass Model can produce
Primordial Black Holes within a mass range compatible with Dark Matter, i.e.
within a mass range 10^{20}g< M_{BH}<10^{27}g.
