论文标题
标量诱导重力波的仪表转换
Gauge transformation of scalar induced gravitational waves
论文作者
论文摘要
标量诱导的重力波（SIGW）在第二阶产生的量规依赖性对标量扰动产生的次级重力波的讨论构成了挑战。我们提供了一个通用公式，该公式在任何规格中都有效，用于计算SIGWS以及在坐标转换下以各个仪表计算的SIGW的关系。将牛顿量规与其他量规的SIGW相关的公式用于计算六个不同仪表中的SIGW。我们发现，牛顿仪，均匀的曲率量规，同步仪和均匀的膨胀仪对SIGW的能量密度产生相同的结果。我们还识别并消除了同步规格中存在的纯仪表模式。在总物质量规和共同的正交仪表中，SIGWS的能量密度增加为$η^2 $。而在均匀的密度仪表中，SIGWS的能量密度增加为$η^6 $。
The gauge dependence of the scalar induced gravitational waves (SIGWs) generated at the second order imposes a challenge to the discussion of the secondary gravitational waves generated by scalar perturbations. We provide a general formula that is valid in any gauge for the calculation of SIGWs and the relationship for SIGWs calculated in various gauges under the coordinate transformation. The formula relating SIGWs in the Newtonian gauge to other gauges is used to calculate SIGWs in six different gauges. We find that the Newtonian gauge, the uniform curvature gauge, the synchronous gauge and the uniform expansion gauge yield the same result for the energy density of SIGWs. We also identify and eliminate the pure gauge modes that exist in the synchronous gauge. In the total matter gauge and the comoving orthogonal gauge, the energy density of SIGWs increases as $η^2$. While in the uniform density gauge, the energy density of SIGWs increases as $η^6$.
