标题： 由原初磁场引起的矢量诱导引力波 显示英文标题

标题： Vector induced Gravitational Waves sourced by Primordial Magnetic Fields

摘要： 在本工作中，我们开发了一个通用的形式化方法，用于研究由一阶矢量度规扰动在二阶下引起的张量扰动，将这些引起的张量模式称为$\textit{vector-induced gravitational waves}$（VIGWs）。 值得注意的是，考虑到一种形式为$P_B(k)\propto k^{n_\mathrm{B}}$的类暴胀幂律型磁场功率谱（其中$n_{\rm B}$是磁场谱指数），我们表明，在刚性暴胀后方程状态下，VIGW 信号被增强，最大增强发生在$w=1$。 我们明确地证明这一贡献超过了由一阶磁场引起的引力波。 该VIGW谱在宇宙学视界在再加热结束时交叉的尺度处出现最大值，$k_\mathrm{reh}$，其现今峰值幅度按$\Omega_{\rm GW}(k_{\rm reh},\eta_0)\propto \Delta N_{\rm reh}\times(H_{\rm inf}/M_{\rm Pl})^{8}$变化，其中$H_{\rm inf}$是暴胀结束时的哈勃参数，$\Delta N_{\rm reh}$是暴胀后时期的持续时间，以$e$-折叠为单位。 对于$w=1$（kination）和$n_{\rm B}>-3/2$，还可以得到几乎与$n_{\rm B}$无关的引力波频谱频率标度，形式为$\Omega_{\rm GW}(f,\eta_0)\propto \left(\frac{f}{f_{\rm reh}}\right)^{-2.8}$对于$f>f_\mathrm{reh}\equiv k_\mathrm{reh}/(2\pi)$。最后，我们指出，VIGW信号在小尺度上可以很好地处于多个下一代干涉型引力波任务的探测频段内。 大致来说，对于$H_{\rm inf} \sim O(10^{7})\:\mathrm{GeV}$和$O(10^{14})\:\mathrm{GeV}$，以及$\Delta N_{\rm reh} \sim 15$和$10$，VIGW 信号预计分别可以被 LISA 和 ET 检测到。 显示英文摘要

摘要： In this work, we develop a generic formalism for the study of tensor perturbations induced at second order by first-order vector metric perturbations, dubbing these induced tensor modes $\textit{vector-induced gravitational waves}$ (VIGWs). Notably, considering an inflation-inspired power-law type magnetic field power spectrum of the form $P_B(k)\propto k^{n_\mathrm{B}}$ (where $n_{\rm B}$ is the magnetic spectral index), we show that the VIGW signal is enhanced for stiff post-inflationary EoS, with the maximum enhancement happening for $w=1$. We explicitly demonstrate this contribution is dominant over the first-order magnetically-sourced GWs. The VIGW spectrum exhibits a maximum at around the scale crossing the cosmological horizon at the end of reheating, $k_\mathrm{reh}$, with its present day peak amplitude scaling as $\Omega_{\rm GW}(k_{\rm reh},\eta_0)\propto \Delta N_{\rm reh}\times(H_{\rm inf}/M_{\rm Pl})^{8}$, where $H_{\rm inf}$ is the Hubble parameter at the end of inflation and $\Delta N_{\rm reh}$ the duration of the post-inflationary era in $e$-folds. For $w=1$ (kination) and $n_{\rm B}>-3/2$, one further obtains a nearly $n_{\rm B}$-independent frequency scaling of the GW spectrum of the form $\Omega_{\rm GW}(f,\eta_0)\propto \left(\frac{f}{f_{\rm reh}}\right)^{-2.8}$ for $f>f_\mathrm{reh}\equiv k_\mathrm{reh}/(2\pi)$. Finally, we highlight that the VIGW signal can be well within the detection bands of several next-generation interferometric GW missions at small scales. Indicatively, for $H_{\rm inf} \sim O(10^{7})\:\mathrm{GeV}$ and $O(10^{14})\:\mathrm{GeV}$, and $\Delta N_{\rm reh} \sim 15$ and $10$, the VIGW signal is expected to be detectable by LISA and ET respectively.