Testing Primordial Black Holes as Dark Matter through LISA

Abstract: The idea that primordial black holes (PBHs) can comprise most of the dark matter of the universe has recently reacquired a lot of momentum. Observational constraints, however, rule out this possibility for most of the PBH masses, with a notable exception around $10^{-12} M_\odot$. These light PBHs may be originated when a sizeable comoving curvature perturbation generated during inflation re-enters the horizon during the radiation phase. During such a stage, it is unavoidable that gravitational waves (GWs) are generated. Since their source is quadratic in the curvature perturbations, these GWs are generated fully non-Gaussian. Their frequency today is about the mHz, which is exactly the range where the LISA mission has the maximum of its sensitivity. This is certainly an impressive coincidence. We show that this scenario of PBHs as dark matter can be tested by LISA by measuring the GW two-point correlator. On the other hand, we show that the short observation time (as compared to the age of the universe) and propagation effects of the GWs across the perturbed universe from the production point to the LISA detector suppress the bispectrum to an unobservable level. This suppression is completely general and not specific to our model.

• The paper proposes that ~10⁻¹² M☉ primordial black holes, formed from enhanced curvature perturbations after inflation, could account for dark matter.
• The paper models gravitational wave production predicting a power spectrum peak at mHz frequencies where LISA is optimally sensitive.
• The paper highlights observational challenges including phase decoherence and suppressed bispectrum signals due to limited LISA observation time and cosmic propagation effects.

Primordial Black Holes as Dark Matter and Gravitational Wave Detection by LISA

The hypothesis that primordial black holes (PBHs) could account for dark matter remnants in the universe has been revisited within the context of recent gravitational wave observations. Specifically, this paper explores the potential for PBHs with masses circa $10^{-12} M_\odot$ to be constituents of dark matter and investigates how the Laser Interferometer Space Antenna (LISA) can be utilized to test this model.

Core Thesis

The study examines a scenario where primordial black holes form due to enhanced curvature perturbations following inflation, yet constrained within specific mass limits, notably avoiding extensive exclusion due to observational data over a significant range. A critical pivot in the narrative is that PBHs of a lightweight nature, around $10^{-12} M_\odot$, which might have formed when large curvature perturbations, created during inflation, re-enter the horizon during the radiation era. This reentry leads to the production of gravitational waves (GWs) at a frequency range where LISA's sensitivity peaks, a fortuitous alignment that establishes LISA as a unique observatory for such phenomena.

Methodology and Theoretical Implications

The analysis is based on deriving the production of GWs during the formation of PBHs, assuming these perturbations generate non-Gaussian GWs due to the inherent non-linear processes involved. The study suggests calculating the power spectrum of these GWs and proposes using LISA to detect the GW power spectrum maximum sensitivity region around the mHz frequency—a frequency correlated with PBHs of $10^{-12} M_\odot$.

Strong numerical results indicate that if PBHs represent dark matter, LISA can measure the corresponding GW signature via its two-point correlator. However, the study brings awareness to a notable suppression in observing the bispectrum of these GWs due to LISA's limited observational time frame, as well as the propagation effects resulting in decreased coherence across the cosmological horizon.

Observational Challenges

The paper discusses the challenges in correlating GW observation with primordial phenomena. The short observation phase relative to the universe's age results in a substantial reduction of visible indications of non-Gaussianity in the GW spectrum, primarily attributed to phase decoherence as GWs traverse the universe. The calculation outlines how this interferes with the three-point correlator's effectiveness.

Further, general propagation effects in the perturbed universe impose limitations on observational resolutions, where the initial phase coherence is effectively mitigated by large-scale cosmic structures—leading to diminished observable bispectrum signals.

Conclusion and Prospects

Concluding that LISA's sensitivity can capture and potentially confirm certain PBH dark matter models by detecting relevant GWs, this paper underlines crucial implications for understanding the early universe's structure and dynamics. Future research can build upon these findings, focusing on improving methods for observing high-precision GW signals that might offer better insight into exotic cosmological models and other potential phenomena indicated by GW characteristics beyond Gaussian distribution.

While the study recognizes current technological constraints in harnessing full observational data regarding GW bispectrum, it emphasizes the interdisciplinary potential within astroparticle physics and cosmology—to unravel the enigmatic makeup of our universe through observational advances and theoretical refinements. Continued exploration within this domain could arguably redefine comprehensions of both PBHs and their correlation with the cosmos's dark matter paradigm.