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arXiv 2210.03476astro-ph.COgr-qc
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来自标量诱导引力波的宇宙学约束对原初黑洞的影响

Implications for primordial black holes from cosmological constraints on scalar-induced gravitational wave

Junsong Cang, Yin-Zhe Ma, Yu Gao

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AI总结：

本文利用宇宙学对相对论自由度的约束，通过标量诱导引力波限制原初黑洞丰度及小尺度曲率扰动，并结合CMB、BAO和BBN数据排除了大质量原初黑洞作为暗物质主要成分的可能性。

摘要：

早期宇宙中足够大的标量扰动可以形成过密区域，这些区域坍缩为原初黑洞（PBH）。这一过程伴随着标量诱导引力波（SIGW）的发射，这些引力波表现为额外的辐射成分，从而对相对论自由度（$N_{\rm{eff}}$）产生贡献。我们表明，对 $N_{\rm{eff}}$ 的宇宙学约束可以用来对这一特定情形下产生的原初黑洞以及相关的小尺度曲率扰动（$\mathcal{P}_{\mathcal{R}}(k)$）施加严格的限制。我们表明，结合宇宙微波背景（CMB）、重子声学振荡（BAO）和大爆炸核合成（BBN）数据集，可以排除峰值质量 $M_{\bullet} \in [5 \times 10^{5}, 5 \times 10^{10}]\\,{\rm M}_{\odot}$ 的超大质量原初黑洞作为暗物质的主要成分，而具体约束取决于原初黑洞质量分布的形状。未来的 CMB 任务如 CMB-S4 可以将这一约束窗口扩大到更大的范围 $M_{\bullet} \in [8 \times 10^{-5}, 5 \times 10^{10}]\\,{\rm M}_{\odot}$，覆盖亚恒星质量。这些对原初黑洞的限制对应于在 $k \in [10, 10^{22}]\\ {\rm{Mpc^{-1}}}$ 尺度上对 $\mathcal{P}_{\mathcal{R}}$ 的更严格约束，该尺度远小于直接 CMB 和大尺度结构功率谱所探测的尺度。

英文摘要：

Sufficiently large scalar perturbations in the early Universe can create over-dense regions that collapse into primordial black holes (PBH). This process is accompanied by the emission of scalar-induced gravitational waves (SIGW) that behave like an extra radiation component, thus contributing to the relativistic degrees of freedom ($N_{\rm{eff}}$). We show that the cosmological constraints on $N_{\rm{eff}}$ can be used to pose stringent limits on PBHs created from this particular scenario as well as the relevant small-scale curvature perturbation ($\mathcal{P}_{\mathcal{R}}(k)$). We show that the combination of cosmic microwave background (CMB), baryon acoustic oscillation (BAO) and Big-Bang nucleosynthesis (BBN) datasets can exclude supermassive PBHs with peak mass $M_{\bullet} \in [5 \times 10^{5}, 5 \times 10^{10}]\,{\rm M}_{\odot}$ as the major component of dark matter, while the detailed constraints depend on the shape of the PBHs mass distribution. The future CMB mission like CMB-S4 can broaden this constraint window to a much larger range $M_{\bullet} \in [8 \times 10^{-5}, 5 \times 10^{10}]\,{\rm M}_{\odot}$, covering sub-stellar masses. These limits on PBH correspond to a tightened constraint on $\mathcal{P}_{\mathcal{R}}$ on scales of $k \in [10, 10^{22}]\ {\rm{Mpc^{-1}}}$, much smaller than those probed by direct CMB and large-scale structure power spectra.

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