# Gravitational Waves in f(R) Gravity Power Law Model

## TL;DR

This paper explores the polarization modes of gravitational waves in a specific f(R) gravity model, revealing the conditions under which scalar and breathing modes appear, and how their properties depend on the model parameters.

## Contribution

It demonstrates the existence and behavior of scalar polarization modes in f(R) gravity power law models, highlighting the dependence on background curvature and model parameters.

## Key findings

- Massive scalar mode exists for certain n values.
- No scalar mode for n=2, but a breathing mode appears.
- Scalar field mass varies with n between 1 and 2.

## Abstract

We investigate the different polarization modes of Gravitational Waves (GWs) in $f(R)$ gravity power law model in de Sitter space. It is seen that the massive scalar field polarization mode exists in this model. The mass of the scalar field depends highly on the background curvature and the power term $n$. However, we found that the model doesnot exhibit a massive scalar mode for $n=2$ and instead it shows a breathing mode in addition to the tensor plus and cross modes. Thus mass of the scalar field is found to vary with $n$ within the range $1 \leq n \leq 2$.