论文标题
自由流中微子对二阶引起重力波的影响
Impact of the free-streaming neutrinos to the second order induced gravitational waves
论文作者
论文摘要
详细研究了自由流中微子对二阶重力波的阻尼效应。我们解决了玻尔兹曼方程，并给中微子引起的各向异性应力延伸到二阶。考虑了一阶张量及其与标量扰动引起的重力波的耦合。我们给出阻尼内核函数的分析方程，并最终获得能量密度谱。结果表明，自由流中微子抑制了低频引力波的密度光谱，并在红外区域（$ k \ ll k _*$）扩大了对数斜率$ n $。对于$ k _*\ sim 10^{ - 7} $ hz的光谱，$ k <k _*$范围内的阻尼效果很重要。第一阶和第二订单的综合效果可以将幅度降低$ 30 \％$，并使$ n $从$ 1.54 $跃升至$ k \ sim 10^{ - 9} $ Hz的$ 1.63 $，这可能由Pulsar Time Arrays（PTA）探索。
The damping effect of the free-streaming neutrinos on the second order gravitational waves is investigated in detail. We solve the Boltzmann equation and give the anisotropic stress induced by neutrinos to second order. The first order tensor and its coupling with scalar perturbations induced gravitational waves are considered. We give the analytic equations of the damping kernel functions and finally obtain the energy density spectrum. The results show that the free-streaming neutrinos suppress the density spectrum significantly for low frequency gravitational waves and enlarge the logarithmic slope $n$ in the infrared region ($k \ll k_*$) of the spectrum. For the spectrum of $k_*\sim 10^{-7}$Hz, the damping effect in the range of $k<k_*$ is significant. The combined effect of the first and second order could reduce the amplitude by $30\%$ and make $n$ jump from $1.54$ to $1.63$ at $k\sim 10^{-9}$Hz, which may be probed by the pulsar timing arrays (PTA) in the future.
