The Primordial Black Hole Dark Matter - LISA Serendipity

Abstract: There has recently been renewed interest in the possibility that the dark matter in the universe consists of primordial black holes (PBHs). Current observational constraints leave only a few PBH mass ranges for this possibility. One of them is around $10^{-12} M_\odot$. If PBHs with this mass are formed due to an enhanced scalar-perturbation amplitude, their formation is inevitably accompanied by the generation of gravitational waves (GWs) with frequency peaked in the mHz range, precisely around the maximum sensitivity of the LISA mission. We show that, if these primordial black holes are the dark matter, LISA will be able to detect the associated GW power spectrum. Although the GW source signal is intrinsically non-Gaussian, the signal measured by LISA is a sum of the signal from a large number of independent sources suppressing the non-Gaussianity at detection to an unobservable level. We also discuss the effect of the GW propagation in the perturbed universe. PBH dark matter generically leads to a detectable, purely isotropic, Gaussian and unpolarised GW signal, a prediction that is testable with LISA.

• The paper introduces a model where PBHs of ~10⁻¹² solar masses, formed by enhanced inflationary perturbations, could constitute dark matter.
• It employs Gaussian smoothing of density contrasts to derive a critical mass fraction and predicts a gravitational wave peak in the mHz range compatible with LISA's sensitivity.
• Detecting a Gaussian, isotropic gravitational wave background would validate the PBH dark matter hypothesis and prompt a re-evaluation of standard inflationary cosmology.

Overview of "The Primordial Black Hole Dark Matter - LISA Serendipity"

The paper discusses the potentiality that primordial black holes (PBHs) could constitute a major component of dark matter in the universe. A particular focus is placed on PBHs with masses around $10^{-12} M_\odot$, a mass range that is not currently constrained by observations. This focus aligns serendipitously with the sensitivity of the Laser Interferometer Space Antenna (LISA), a space-based gravitational wave detector.

Core Hypothesis and Predictions

The hypothesis that PBHs might form all or part of dark matter revisits longstanding questions about the origins of cosmic dark matter. The researchers propose that if PBHs formed due to enhanced scalar-perturbation amplitudes, such formations would by necessity be accompanied by the generation of gravitational waves (GWs). These GWs are expected to peak in frequency in the millihertz (mHz) range, coinciding with LISA's optimal sensitivity.

Yet, the paper argues that while the GW source signal is intrinsically non-Gaussian, the signal detected by LISA would appear Gaussian due to summation over many independent sources. The authors forecast that LISA will be able to detect this GW signal as a Gaussian, isotropic, and unpolarised background, if PBHs indeed comprise dark matter.

Methodological Approach

The generation of PBHs in the early universe is connected to inflating perturbations large enough to cause collapse back into PBHs upon horizon re-entry. The paper details the derivation of the critical mass fraction and the correlation between PBH mass and GW peak frequency.

• The calculations rely on defining the comoving curvature perturbation power spectrum and using the Dirac delta function as an idealized representation.
• By employing a Gaussian window function, the document elaborates on smoothing the density contrasts.
• A critical mass fraction necessary for the universe to evolve into PBHs is articulated, with a specific parameterization for the current dark matter fraction associated with PBHs.
• The methodology also covers the gravitational wave equation of motion derived from second-order perturbations, establishing their significance and potential detectability.

Implications and Future Speculations

The authors discuss the implications of detectable GWs related to PBHs' formation, focusing on LISA's capabilities:

• Practical Implications: If LISA identifies the GW signature hypothesized, it would validate the PBH dark matter model. This would be both a cost-effective and theoretically efficient model, needing no beyond-standard model physics.
• Theoretical Implications: Such findings would challenge current understandings of the inflationary universe and necessitate revisions to the standard cosmological models. The results could fine-tune measurements of inflation-derived perturbations and offer insights into small-scale structures in the early universe.
• Future Directions: Further research could explore detailed GW power spectrum shapes and their potential to distinguish between different sources, such as phase transitions. Additionally, if constraints on PBH abundance change with future astrophysical observations, these models may need recalibration, but underlying conclusions about detectability remain robust.

Conclusions

The research proposes a viable scenario where primordial black holes of $10^{-12} M_\odot$ comprise the universe’s dark matter and produce a detectable GW background. This proposition is especially testable with the upcoming LISA mission. Despite the intrinsic features of the GW source, the signals detected will be isotropic and Gaussian due to the Central Limit Theorem effects and life-cycle measurements covering numerous Hubble patches. This study paves the way for LISA to potentially unravel the dark matter enigma in the broader cosmological context.