The impact of non-Gaussianity when searching for Primordial Black Holes with LISA

TL;DR

This work assesses how non-Gaussian primordial perturbations and astrophysical foregrounds affect the use of scalar-induced gravitational waves in the LISA band as a probe of asteroid-mass primordial black hole dark matter. By modeling local primordial NG with a quadratic term, employing a log-normal scalar power spectrum, and distinguishing Gaussian-disconnected from NG-connected GW contributions, the authors connect SIGW measurements to PBH abundances while enforcing perturbativity bounds. Their results show that even non-detections by LISA would strongly constrain the scalar power spectrum only in the Gaussian or mildly NG regime; sizable non-Gaussianity can reopen PBH windows, while foregrounds further relax constraints. Bayesian inference with mock SIGW detections reveals that although LISA can pin down the power-spectrum parameters with high precision, the inferred PBH abundance is extremely sensitive to the uncertain $f_{ m NL}$, potentially spanning up to ~30 orders of magnitude. Overall, the paper highlights that robust conclusions about asteroid-mass PBHs require external constraints on primordial non-Gaussianity and careful treatment of astrophysical foregrounds when interpreting SIGW data.

Abstract

LISA can observe cosmological millihertz (mHz) gravitational wave (GW) backgrounds that may offer a decisive test for asteroid-mass primordial black hole (PBH) dark matter (DM). In standard scenarios, failing to detect a scalar-induced gravitational wave (SIGW) background would exclude the last viable window for PBH DM formed through critical collapse. We show that this conclusion becomes much weaker in the presence of astrophysical foregrounds and strongly non-Gaussian primordial density perturbations, by studying how these phenomena affect the link between SIGWs and PBHs, and reevaluate LISA's sensitivity to asteroid-mass PBHs. In addition, we analyse the interplay between PBHs and SIGWs to gain further insights into the nature of primordial non-Gaussianity. We find that uncertainties in $f_{\rm NL}$ can induce substantial uncertainties in the PBH abundance, which ultimately limits LISA's capacity to fully probe the asteroid-mass PBH DM window.

Figures (8)

• Figure 1: Comparison between the perturbative expansion of the non-Gaussian field $\zeta$ as in Eq. \ref{['Eq::local_NG']} and the full functional form $\zeta = F(\zeta_G)$ for two benchmark scenarios: USR and curvaton models. The coefficients $\mathcal{C}_1$ and $\mathcal{C}_2$ are shown for $f_{\mathrm{NL}} = 1$ (top) and $f_{\mathrm{NL}} = 10$ (bottom).
• Figure 2: Left panel: Amplitude $A$ of the power spectrum, e.g. Eq. \ref{['eq:PSlog']}, that is required to get respectively $f_{\rm PBH}=1$ (solid lines) and $f_{\rm PBH}=10^{-3}$ (dashed lines) using TS (red) and the PT (green) as a function of the power spectrum width $\Delta$, assuming negligible primordial NGs, i.e $f_{\rm NL}=0$. Right panel: Amplitude $A$ required to obtain $f_{\rm PBH} = 1$ for different $f_{\rm NL}$ and different benchmark cases for the width $\Delta$, within the TS approach. The excluded regions by the perturbativity condition, Eq. \ref{['eq:PerturbCri1']}, are reported in grey while the perturbativity condition for the USR and curvaton cases are shown as solid and dashed black lines, respectively. In dark grey we report region excluded by the naive condition usually adopted in literature, i.e. $(3/5)^2f_{\rm NL}^2 A < 1$. In the left and right panels, we use the benchmark values $k_*=10^{12.5}$$\textrm{Mpc}^{-1}$ and $k_*=10^{8}$$\textrm{Mpc}^{-1}$, respectively.
• Figure 3: Constraints and prospective sensitives on the primordial scalar power spectrum for current and future GW experiments. The curvature perturbations are assumed Gaussian statistics and to follow log-normal power spectra with for two different widths, $\Delta =0.$ (solid lines) and $\Delta =0.9$ (dashed lines). The existing constraints for Planck+ACTACT:2025tim and Ly -$\alpha$lyman are taken directly from their respective analyses, while for FIRASChluba:2012weChluba:2013dnaIovino:2024tyg and NANOGrav15NANOGrav:2023gorNANOGrav:2023hdeIovino:2024tyg they are computed using the latest data and assuming our template for the primordial power spectrum. The sensitivities are shown for SKAJanssen:2014dka, LISALISA:2017pwj, AEDGEAEDGE:2019nxb, TianQinTianQin:2015yph, ETMaggiore:2019uih, CEReitze:2019iox and aLIGOLIGOScientific:2016wof estimated using ${\rm SNR}_{\rm th}=10$ and an observation time of $1$ year. The light grey lines indicate the upper bound on $A$ due to the PBH overproduction (assuming the TS formalism).
• Figure 4: Projected sensitivities on the amplitude of the scalar power spectrum a detection of a SIGW signal from LISA, with ${\rm SNR} = 10$ and 4 years of observation time. Solid lines represent the bounds when the presence of foregrounds is neglected, while dotted lines represent the bounds when foregrounds are included. The dot-dashed lines indicate $f_{\rm PBH} = 1$ for different $f_{\rm NL}$.
• Figure 5: Contour plot of the SNR computed in the Gaussian approximation ($f_{\rm NL} = 0$), assuming a log-normal power spectrum with width $\Delta = 0.3$, shown as a function of the peak position $k_*$ and the amplitude $A$. The panel also includes four selected configurations (colored dots) used as injected signal for the MCMC analysis, along with their corresponding 2D 95% confidence contours (dashed colored lines). Two black horizontal lines indicate the threshold values of $A$, as a function of $k_*$, above which PBH overproduction occurs, according to the TS (solid) and PT (dashed) formalisms.