标题： 脉冲星阵列观测数据的诱导引力波解释：一般状态方程的完整研究 显示英文标题

标题： Induced Gravitational Wave interpretation of PTA data: a complete study for general equation of state

摘要： 我们系统研究了脉冲星阵列合作组织报告的可能引力波背景的诱导引力波解释，考虑了早期宇宙未知的状态方程$w$。 我们使用公开可用的\textsc{PTArcade}代码结合\textsc{SIGWfast}对 NANOGrav 数据进行了贝叶斯分析以数值积分诱导引力波谱。 我们关注两种情况：单色和对数正态的原初扰动谱。 对于对数正态谱，我们表明，当引力波峰值接近脉冲星阵列窗口时，结果对$w$不太敏感；然而，当只有红外幂律尾部贡献时，辐射主导时期超出了$2\sigma$的轮廓范围。 对于单色谱，$2\sigma$的界限得到$0.1\lesssim w\lesssim0.9$，这意味着辐射主导时期接近中心值。 我们还利用峰值形式探讨了原初黑洞（PBH）的对应物。 我们表明，一般来说，较大的宽度和更硬的状态方程可以减轻PBH过量产生的问题。 不存在PBH过量产生要求单色谱的 $w\gtrsim0.42$至少达到 2-$\sigma$水平。 此外，结合宇宙微波背景的限制，我们发现通常情况下，PBH对应的质量范围被限定在 $10^{-5} M_\odot\lesssim M_{\rm PBH}\lesssim10^{-1} M_\odot$之内。 最后，我们发现脉冲星定时阵列信号可以解释由OGLE报告的 $0.42\lesssim w\lesssim 0.50$的微引力透镜事件。 我们的工作展示了未来数据分析中，广义 $w$的诱导引力波和原初黑洞的完整处理方法。 显示英文摘要

摘要： We thoroughly study the induced gravitational wave interpretation of the possible gravitational wave background reported by PTA collaborations, considering the unknown equation of state $w$ of the early universe. We perform a Bayesian analysis of the NANOGrav data using the publicly available \textsc{PTArcade} code together with \textsc{SIGWfast} for the numerical integration of the induced gravitational wave spectrum. We focus on two cases: a monochromatic and a log-normal primordial spectrum of fluctuations. For the log-normal spectrum, we show that, while the results are not very sensitive to $w$ when the GW peak is close to the PTA window, radiation domination is out of the $2\sigma$ contours when only the infra-red power-law tail contributes. For the monochromatic spectrum, the $2\sigma$ bounds yield $0.1\lesssim w\lesssim0.9$ so that radiation domination is close to the central value. We also investigate the primordial black hole (PBH) counterpart using the peak formalism. We show that, in general terms, a larger width and stiffer equation of state alleviates the overproduction of PBHs. No PBH overproduction requires $w\gtrsim0.42$ up to 2-$\sigma$ level for the monochromatic spectrum. Furthermore, including bounds from the cosmic microwave background, we find in general that the mass range of the PBH counterpart is bounded by $10^{-5} M_\odot\lesssim M_{\rm PBH}\lesssim10^{-1} M_\odot$. Lastly, we find that the PTA signal can explain the microlensing events reported by OGLE for $0.42\lesssim w\lesssim 0.50$. Our work showcases a complete treatment of induced gravitational waves and primordial black holes for general $w$ for future data analysis.