标题： 脉冲星计时阵列数据的诱导引力波解释：对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： 我们全面研究了PTA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}代码以及\textsc{SIGWfast}对诱导引力波谱进行数值积分，对NANOGrav数据进行了贝叶斯分析。 我们关注两种情况：单色和对数正态原初谱。 对于对数正态谱，我们表明，当引力波峰接近PTA窗口时，结果对$w$不太敏感，但仅当红外幂律尾部贡献时，辐射主导将超出$2\sigma$的轮廓。 对于单色谱，$2\sigma$的限制产生$0.1\lesssim w\lesssim0.9$，使得辐射主导接近中心值。 我们还利用峰值形式研究了原初黑洞（PBH）的对应情况。 我们表明，一般来说，更大的宽度和更刚性的状态方程可以缓解PBH的过度产生。 没有PBH过量产生需要$w\gtrsim0.42$达到2-$\sigma$级别对于单色谱。此外，包括来自宇宙微波背景的限制，我们发现PBH对应的质量范围由$10^{-5} M_\odot\lesssim M_{\rm PBH}\lesssim10^{-1} M_\odot$限定。最后，我们发现PTA信号可以解释OGLE报告的微透镜事件对于$0.42\lesssim w\lesssim 0.50$。我们的工作展示了对一般$w$的诱导引力波和原初黑洞的完整处理，以用于未来的数据分析。 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.