Damping of gravitational waves in f(R) gravity

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 $$f(R) = R + \alpha R^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>R</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>=</mml:mo> <mml:mi>R</mml:mi> <mml:mo>+</mml:mo> <mml:mi>α</mml:mi> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> , we investigate the effect of the mass term on wave amplitude decay within the neutrino system. We observe that the tensor mode with $$m = 1 \, \text {eV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mspace/> <mml:mtext>eV</mml:mtext> </mml:mrow> </mml:math> exhibits faster decay compared to other cases, while the scalar mode with $$m = 1 \, \text {eV}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mspace/> <mml:mtext>eV</mml:mtext> </mml:mrow> </mml:math> appears to suppress decay.