Propagating degrees of freedom in f(R) gravity

TL;DR

This paper analyzes the polarization modes of gravitational waves in f(R) gravity, confirming the presence of three modes, including a massive scalar mode, and clarifies the properties of the metric tensor in this theory.

Contribution

It provides a detailed calculation of the polarization modes in f(R) gravity and introduces a new metric tensor satisfying TT conditions.

Findings

Three polarization modes: two tensor and one scalar

No massless breathing mode detected

The scalar mode corresponds to the Ricci scalar

Abstract

We have computed the number of polarization modes of gravitational waves propagating in the Minkowski background in $f(R)$ gravity. This is three of two from transverse-traceless tensor modes and one from a massive trace mode, which confirms the results found in the literature. There is no massless breathing mode and the massive trace mode corresponds to the Ricci scalar. A newly defined metric tensor in $f(R)$ gravity satisfies the transverse-traceless (TT) condition as well as the TT wave equation.