# Gauge invariant formulation of gravitational waves in metric $f(R)$ gravity

## TL;DR

This paper develops a gauge-invariant framework to analyze gravitational wave propagation in metric $f(R)$ gravity, revealing the presence of two additional polarization modes beyond standard tensor modes.

## Contribution

It provides a clear, gauge-invariant formulation of gravitational waves in $f(R)$ gravity and identifies the specific polarization modes introduced by the theory.

## Key findings

- Two additional polarization modes: breathing and longitudinal.
- Explicit connection between extra degrees of freedom and polarization modes.
- Gauge-invariant formalism clarifies gravitational wave characteristics in $f(R)$ gravity.

## Abstract

We analyze the gravitational waves propagation in metric $f(R)$ theories of gravity. In particular, adopting a gauge invariant formalism we clearly determine the exact propagating degrees of freedom. Then, investigating their effects on test masses via geodesic deviation equation, we show that the additional dynamical degree contained in such extended formulations is actually responsible for two distinguished polarizations, corresponding to a breathing and a longitudinal mode, respectively.