物质主导时期的三阶标量诱导引力波：长期增长及其对原初黑洞主导的启示
Third-order scalar induced gravitational waves during a matter-dominated era: secular growth and implications for primordial black hole domination
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中文总结 AI 辅助
本研究解析计算了物质主导时期三阶标量诱导引力波的核函数，发现其频谱呈x^6长期增长，并利用无反作用条件将原初黑洞初始丰度约束强化至约4.6×10^-7，比二阶结果强三个数量级。
中文摘要 AI 辅助
我们研究了物质主导（MD）时期的三阶标量诱导引力波（SIGWs）。我们将源分为四个部分——由三个一阶标量构成，以及由一阶标量乘以二阶张量、矢量和标量扰动构成——并以闭合形式解析地获得了所有四个核函数。与辐射主导时期的对应物不同，MD核函数随时间长期增长，这转化为频谱的快速增长，在$x\equiv k\eta\gg1$时，$\Omega^{(3)}_{\mathrm{GW}}\propto x^{6}$ 对比 $\Omega^{(2)}_{\mathrm{GW}}\propto x^{2}$。我们针对一般原初谱推导出三阶功率谱为五重积分，并对单色谱进行了数值评估，其中来自二阶矢量源的所有贡献均恒为零。作为应用，我们考虑了由原初黑洞（PBHs）在其蒸发之前驱动的早期MD时期。要求诱导引力波不对宇宙学扰动产生反作用，$\int\mathrm{d}\ln k\\, \Omega^{\mathrm{tot}}_{\mathrm{GW}}<1$，从而将初始PBH丰度约束为$\Omega_{\mathrm{PBH},f}\lesssim4.6\times10^{-7}\\, (m_{\mathrm{PBH}}/10^{7}\\,\mathrm{g})^{-0.48}$，这比仅考虑二阶效应的约束强约三个数量级。我们的结果表明，在足够长的MD时期中，高阶SIGWs不可避免地变得非微扰，这对涉及早期物质主导的情景具有重要意义。
英文摘要
We investigate scalar induced gravitational waves (SIGWs) at third-order during a matter-dominated (MD) era. We classify the sources into four parts---built from three first-order scalars, and from a first-order scalar times the second-order tensor, vector, and scalar perturbations---and obtain all four kernel functions analytically in closed form. Unlike their radiation-dominated counterparts, the MD kernel functions grow secularly, translating into a rapid growth of the spectrum, $Ω^{(3)}_{\mathrm{GW}}\propto x^{6}$ versus $Ω^{(2)}_{\mathrm{GW}}\propto x^{2}$ at $x\equiv kη\gg1$. We derive the third-order power spectrum as a five-fold integral for a general primordial spectrum, and evaluate it numerically for a monochromatic one, where all contributions from the second-order vector source vanish identically. As an application, we consider the early MD era driven by primordial black holes (PBHs) before their evaporation. Requiring that the induced gravitational waves do not backreact on the cosmological perturbations, $\int\mathrm{d}\ln k\, Ω^{\mathrm{tot}}_{\mathrm{GW}}<1$ then bounds the initial PBH abundance as $Ω_{\mathrm{PBH},f}\lesssim4.6\times10^{-7}\, (m_{\mathrm{PBH}}/10^{7}\,\mathrm{g})^{-0.48}$, about three orders of magnitude stronger than the second-order-only bound. Our results indicate that higher-order SIGWs inevitably become nonperturbative during a sufficiently long MD era, with important implications for scenarios involving an early matter domination.
发表机构
- Huai’an University（淮阴工学院）
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