New probe of non-Gaussianities with primordial black hole induced gravitational waves

New probe of non-Gaussianities with primordial black hole induced gravitational waves

1 Mar 2024 | Theodoros Papanikolaou, Xin-Chen He, Xiao-Han Ma, Yi-Fu Cai, Emmanuel N. Saridakis, Misao Sasaki
This paper proposes a novel method to probe primordial non-Gaussianities (NGs) through the observation of gravitational waves (GWs) induced by ultra-light primordial black holes (PBHs). The existence of primordial NGs can leave imprints on the clustering properties of PBHs and the spectral shape of induced GW signals. The authors focus on a scale-dependent local-type NG and identify a distinct double-peaked GW energy spectrum that may fall into the frequency bands of upcoming GW observatories, such as LISA, ET, SKA, and BBO. This signal can serve as a novel portal for probing primordial NGs. By combining BBN bounds on the GW amplitude, the authors find a joint limit on the product of the effective nonlinearity parameter for the primordial tri-spectrum, denoted by $\bar{\tau}_{NL}$, and the primordial curvature perturbation power spectrum $\mathcal{P}_{\mathcal{R}}(k)$, which is given by $\bar{\tau}_{\mathrm{NL}}\mathcal{P}_{\mathcal{R}}(k) < 4 \times 10^{-20} \Omega_{\mathrm{PBH,f}}^{-17/9} \left( \frac{M_{\mathrm{PBH}}}{10^{16} \mathrm{g}} \right)^{-17/9}$. The paper discusses the implications of PBHs on the early universe, their formation, and the resulting gravitational waves. It also explores the effects of non-Gaussianities on the clustering of PBHs and the resulting GW signals. The authors propose a phenomenological parametrization for the nonlinearity parameter $\tau_{NL}$ and the primordial curvature perturbation spectrum $\mathcal{P}_{\mathcal{R}}(k)$. They show that the induced GW signal can be significantly enhanced at low frequencies due to the non-vanishing trispectrum, in addition to the induced GW signal from the uncorrelated PBH distribution at higher frequencies, forming a bi-peak structure. The authors also derive an analytic approximation for the dominant part of the GW energy spectrum in different k regions of interest. The paper concludes that the proposed probe can provide a novel way to constrain primordial NGs. The results show that the GW amplitude at the two peaks, approximately located at $2k_{d}$ and $2c_{s}k_{UV}$, should be below $10^{-6}$ to avoid constraints from BBN. The authors also derive an upper bound on $\bar{\tau}_{NL}\mathcal{P}_{\mathcal{R}}(k)$, which is given by $\bar{\tau}_{\mathrm{NL}}\mathcal{P}_{\mathcal{R}}\big|_{k=2k_{\mathrm{d}}}This paper proposes a novel method to probe primordial non-Gaussianities (NGs) through the observation of gravitational waves (GWs) induced by ultra-light primordial black holes (PBHs). The existence of primordial NGs can leave imprints on the clustering properties of PBHs and the spectral shape of induced GW signals. The authors focus on a scale-dependent local-type NG and identify a distinct double-peaked GW energy spectrum that may fall into the frequency bands of upcoming GW observatories, such as LISA, ET, SKA, and BBO. This signal can serve as a novel portal for probing primordial NGs. By combining BBN bounds on the GW amplitude, the authors find a joint limit on the product of the effective nonlinearity parameter for the primordial tri-spectrum, denoted by $\bar{\tau}_{NL}$, and the primordial curvature perturbation power spectrum $\mathcal{P}_{\mathcal{R}}(k)$, which is given by $\bar{\tau}_{\mathrm{NL}}\mathcal{P}_{\mathcal{R}}(k) < 4 \times 10^{-20} \Omega_{\mathrm{PBH,f}}^{-17/9} \left( \frac{M_{\mathrm{PBH}}}{10^{16} \mathrm{g}} \right)^{-17/9}$. The paper discusses the implications of PBHs on the early universe, their formation, and the resulting gravitational waves. It also explores the effects of non-Gaussianities on the clustering of PBHs and the resulting GW signals. The authors propose a phenomenological parametrization for the nonlinearity parameter $\tau_{NL}$ and the primordial curvature perturbation spectrum $\mathcal{P}_{\mathcal{R}}(k)$. They show that the induced GW signal can be significantly enhanced at low frequencies due to the non-vanishing trispectrum, in addition to the induced GW signal from the uncorrelated PBH distribution at higher frequencies, forming a bi-peak structure. The authors also derive an analytic approximation for the dominant part of the GW energy spectrum in different k regions of interest. The paper concludes that the proposed probe can provide a novel way to constrain primordial NGs. The results show that the GW amplitude at the two peaks, approximately located at $2k_{d}$ and $2c_{s}k_{UV}$, should be below $10^{-6}$ to avoid constraints from BBN. The authors also derive an upper bound on $\bar{\tau}_{NL}\mathcal{P}_{\mathcal{R}}(k)$, which is given by $\bar{\tau}_{\mathrm{NL}}\mathcal{P}_{\mathcal{R}}\big|_{k=2k_{\mathrm{d}}}
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