Damping of gravitational waves in f(R) gravity

TL;DR

This paper studies how gravitational waves are damped in f(R) gravity, showing that collision damping occurs but Landau damping does not, and analyzing the effects of mass terms on wave decay in cosmological models.

Contribution

It provides a detailed analysis of gravitational wave damping mechanisms in f(R) gravity, including the impact of mass terms in specific models like R + α R^2.

Findings

Landau damping is absent in f(R) gravity.

Collision damping causes wave amplitude decay.

Mass terms influence decay rates of tensor and scalar modes.

Abstract

We investigate the damping of gravitational waves (GW) in $f(R)$ gravity by matter. By applying the kinetic theory, we examine the first-order approximation of the relativistic Boltzmann equation. In the flat spacetime, we derive the evolution equations for waves in $f(R)$ gravity and demonstrate that Landau damping is absent while collision damping is present. In the Friedmann-Robertson-Walker (FRW) cosmology, we also examine the dynamical equations for the two modes. Furthermore, in the model $f(R) = R + \alpha R^2$, we investigate the effect of the mass term on wave amplitude decay within the neutrino system. We observe that the tensor mode with $m = 1 \, \text{eV}$ exhibits faster decay compared to other cases, while the scalar mode with $m = 1 \, \text{eV}$ appears to suppress decay.