Observable Spectra of Induced Gravitational Waves from Inflation

TL;DR

This paper investigates how detecting induced gravitational waves from inflation could constrain small-scale primordial power spectra, focusing on Hilltop and running mass inflation models and their potential to produce observable signals and primordial black holes.

Contribution

It analyzes the detectability of induced gravitational waves from specific inflation models and their implications for primordial black hole formation and dark matter.

Findings

Hilltop models can produce observable gravitational waves within detector ranges.

Running mass models can generate detectable signals but require few e-folds.

Primordial black holes from these models could account for dark matter.

Abstract

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.