Scalar induced gravitational waves in f(R) gravity

TL;DR

This paper explores how f(R) gravity modifies the equations governing second order scalar induced gravitational waves and uses observational data to constrain the model parameters.

Contribution

It derives the modified equations of motion for scalar induced gravitational waves in f(R) gravity and performs a Bayesian analysis using pulsar timing data.

Findings

Modified gravity alters the form of gravitational wave equations.

Additional anisotropic stress affects the source term.

Constraints on the HS model parameters from observational data.

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.