Gravitational Wave signatures of inflationary models from Primordial Black Hole Dark Matter (1707.02441v1)

Abstract: Primordial Black Holes (PBH) could be the cold dark matter of the universe. They could have arisen from large (order one) curvature fluctuations produced during inflation that reentered the horizon in the radiation era. At reentry, these fluctuations source gravitational waves (GW) via second order anisotropic stresses. These GW, together with those (possibly) sourced during inflation by the same mechanism responsible for the large curvature fluctuations, constitute a primordial stochastic GW background (SGWB) that unavoidably accompanies the PBH formation. We study how the amplitude and the range of frequencies of this signal depend on the statistics (Gaussian versus $\chi^2$) of the primordial curvature fluctuations, and on the evolution of the PBH mass function due to accretion and merging. We then compare this signal with the sensitivity of present and future detectors, at PTA and LISA scales. We find that this SGWB will help to probe, or strongly constrain, the early universe mechanism of PBH production. The comparison between the peak mass of the PBH distribution and the peak frequency of this SGWB will provide important information on the merging and accretion evolution of the PBH mass distribution from their formation to the present era. Different assumptions on the statistics and on the PBH evolution also result in different amounts of CMB $\mu$-distortions. Therefore the above results can be complemented by the detection (or the absence) of $\mu$-distortions with an experiment such as PIXIE.

• The paper explains how inflationary density fluctuations produce primordial black holes through both Gaussian and non-Gaussian mechanisms.
• It details how second-order effects lead to stochastic gravitational wave backgrounds that can be observed by PTAs and LISA.
• It shows that SGWB and CMB distortion analyses can constrain PBH mass functions and inflationary parameters, deepening our early universe insights.

Gravitational Wave Signatures from Primordial Black Hole Dark Matter and Inflationary Models

This paper discusses the intricate relationship between primordial black holes (PBHs) and gravitational waves (GWs) within certain inflationary frameworks. It examines the ways in which stochastic gravitational wave backgrounds (SGWB), which are inherently tied to primordial conditions, offer a probe into the early universe's mechanisms of PBH production. Specifically, it explores how the dynamics of large curvature fluctuations, generated during inflation and subsequently re-entering the horizon during the radiation era, can lead to the formation of PBHs that act as viable dark matter candidates.

Key Contributions

The paper offers several theoretical insights and predictions regarding GWs and their connections to PBHs:

1. Mechanism of PBH Formation: It elaborates on multiple proposed mechanisms by which high-density fluctuations during inflation can lead to PBH formation. This involves either Gaussian or non-Gaussian statistics of the primordial perturbations, influenced by various features in the inflationary potential, such as sharp changes or multiple stages of inflation.
2. Stochastic Gravitational Wave Backgrounds: The paper highlights the generation of SGWBs from second-order effects due to enhanced scalar modes and how these waves give rise to a detectable GW signal that could be within reach of Pulsar Timing Arrays (PTA) and the Laser Interferometer Space Antenna (LISA).
3. Implications for Detection: The analysis delineates how SGWB measurements, alongside Cosmic Microwave Background (CMB) spectrum distortions, could provide constraints on the mass distribution of PBHs, and their subsequent merger and accretion histories. These constraints could unveil information on the primordial density perturbations and their statistical characteristics.
4. Gaussian vs. Non-Gaussian Statistics: A significant part of the paper focuses on the statistical nature of scalar perturbations—examining Gaussian models versus more complex non-Gaussian distributions resulting from higher-order interactions or non-standard inflation scenarios. The authors specify conditions under which different types of PBH clusters and GW signatures are expected.

Numerical Insights and Theoretical Implications

The paper includes robust numerical simulations and theoretical derivations to predict the GW spectra for different inflationary models. It suggests that PTAs have the potential to significantly probe a wide range of PBH masses, particularly those around 10 solar masses, due to their strong GW signatures in the nanohertz frequency range. Moreover, the results indicate that different assumptions regarding the evolution of the PBH mass function, such as accretion and merging, affect the observed GW spectrum. This is crucial for isolating the primordial features versus evolutionary effects in observational data.

Future Applications and Considerations

The findings add a layer of depth to our understanding of how inflationary models and PBH dark matter might be connected through gravitational wave observations. Future detections or non-detections of expected SGWB signals by LISA or PTA could further constrain the parameter space of viable inflationary models and the role of PBHs as dark matter constituents. Additionally, the interplay between SGWBs and CMB distortions offers another avenue for cross-validation of paradigms in early universe cosmology.

In conclusion, the paper presents a comprehensive analysis of the theoretical implications of inflationary cosmologies on gravitational waves and their potential to act as a tracer for primordial black holes and, by extension, dark matter. It underscores the importance of gravitational wave astronomy as an indispensable tool for probing the conditions present during the universe’s nascent stages.