Observable Spectra of Induced Gravitational Waves from Inflation (1203.4663v2)

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.

Overview of "Observable Spectra of Induced Gravitational Waves from Inflation"

The paper under review, entitled "Observable Spectra of Induced Gravitational Waves from Inflation," explores significant theoretical advancements in cosmology, focusing on the prospects of detecting gravitational waves (GWs) induced by primordial perturbations during inflation. Authored by Laila Alabidi, Kazunori Kohri, Misao Sasaki, and Yuuiti Sendouda, the paper primarily investigates the potential observational implications of small-scale primordial perturbations and their role in inflationary models, particularly those predicting enhanced power spectra on such scales, like the Hilltop-type and running mass models.

Key Contributions

The paper contributes to inflation model building by addressing an observable consequence of enhanced power spectra at small scales: induced gravitational waves. The Cosmic Microwave Background (CMB) data primarily constrains large-scale perturbations; however, small-scale constraints remain elusive due to astrophysical factors like primordial black hole (PBH) production. The authors propose using induced GWs as a probe for these small-scale perturbations, with space-based interferometers like LISA, BBO, and DECIGO offering sufficient sensitivity for potential detection.

Methodology and Analysis

The theoretical framework is based on assessing the gravitational wave spectra generated by different small-scale spectral enhancements. The paper emphasizes two inflationary models known for generating such enhancements:

1. Hilltop-type models - where scalar fields traverse potentials with steep inclines, which can lead to increased small-scale perturbations.
2. Running mass models - where the inflaton mass evolves, inducing variations in the spectral index across scales.

These models were scrutinized for their capacity to produce detectable induced gravitational waves within the detectable range of modern GW observatories.

Results and Findings

• Hilltop-type Models: These models can yield induced gravitational waves within BBO and DECIGO's observational range. In particular, models with integral potential powers provide a feasible inflationary scenario, maintaining adequate e-folds without violating PBH limits.
• Running Mass Models: While capable of generating a significant GW spectrum, such models require an early termination of inflation (insufficient e-folds) unless specific conditions of the Universe's thermal history are assumed. This limits the practicality of detecting their resulting gravitational wave spectrum under current observational limits.

Implications

The outcomes propose a tangible method to link the early universe's inflationary conditions to observational signatures—induced GWs. This connection provides alternative avenues beyond the current CMB constraints, potentially leading to refined inflationary models if detected.

Speculation on Future Developments

Future advancements in gravitational wave detection, particularly with DECIGO, BBO, and a revamped LISA, may provide empirical data to decisively confirm or refute these theoretical models. Such advancements could help discriminate between inflationary models predicting similar CMB outcomes but divergent small-scale behaviors.

Conclusions

The paper presents a compelling case for the role of induced gravitational waves as observational proxies for small-scale inflationary perturbations. It encourages leveraging space-based GW observatories to probe these phenomena, which hitherto remain unresolved by traditional astrophysical observations. This approach promises significant strides in validating or constraining inflationary model space, paving the way for a deeper cosmological understanding of the early universe's fabric.