Friction in Gravitational Waves: a test for early-time modified gravity

Abstract

Modified gravity theories predict in general a non standard equation for the propagation of gravitational waves. Here we discuss the impact of modified friction and speed of tensor modes on cosmic microwave polarization B modes. We show that the non standard friction term, parametrized by \(\alpha_{M}\), is degenerate with the tensor-to-scalar ratio \(r\), so that small values of \(r\) can be compensated by negative constant values of \(\alpha_M\). We quantify this degeneracy and its dependence on the epoch at which \(\alpha_{M}\) is different from the standard, zero, value and on the speed of gravitational waves \(c_{T}\). In the particular case of scalar-tensor theories, \(\alpha_{M}\) is constant and strongly constrained by background and scalar perturbations, \(0\le \alpha_{M}< 0.01\) and the degeneracy with \(r\) is removed. In more general cases however such tight bounds are weakened and the B modes can provide useful constraints on early-time modified gravity.