JCAP, 12, 021 (2024)

Scalar induced gravitational waves in f(R) gravity

Jing-Zhi Zhou¹, Yu-Ting Kuang^2,3, Di Wu^2,4, Fei-Yu Chen¹, Hong Lü^1,5and Zhe Chang^2,3

1 Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University, Tianjin 300350, China.

2 Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China.

3 University of Chinese Academy of Sciences, Beijing 100049, China.

4 School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences, Hangzhou 310024, China.

5 Joint School of National University of Singapore and Tianjin University, International Campus of Tianjin University, Binhai New City, Fuzhou 350207, China.

* zhoujingzhi@tju.edu.cn

Abstract

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.