We investigate the first and second order cosmological perturbation equations in f(R) modified gravity theory and provide the equation of motion of second order scalar induced gravitational waves. We find that the effects of modified gravity not only change the form of the equation of motion of second order scalar induced gravitational waves but also contribute an additional anisotropic stress tensor, composed of first order scalar perturbations, to the source term of the gravitational waves. We calculate the energy density spectrum of second order scalar induced gravitational waves in the HS model. Utilizing current pulsar timing array observational data, we perform a rigorous Bayesian analysis of the parameter space of the HS model.

中文翻译：

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f（R） 重力下的标量感应引力波


我们研究了 f（R） 修正引力理论中的一阶和二阶宇宙学扰动方程，并提供了二阶标量感应引力波的运动方程。我们发现，修正引力的影响不仅改变了二阶标量感应引力波的运动方程的形式，而且还为引力波的源项贡献了一个额外的各向异性应力张量，该张量由一阶标量扰动组成。我们在 HS 模型中计算了二阶标量感应引力波的能量密度谱。利用当前的脉冲星时序阵列观测数据，我们对 HS 模型的参数空间进行了严格的贝叶斯分析。