Measuring the speed of cosmological gravitational waves

In general relativity gravitational waves propagate at the speed of light, however in alternative theories of gravity that might not be the case. We study the effects of a modified speed of gravity, $c_T^2$, on the B-modes of the Cosmic Microwave Background (CMB) anisotropy in polarisation. We find that a departure from the light speed value would leave a characteristic imprint on the BB spectrum part induced by tensors, manifesting as a shift in the angular scale of its peaks. We derive constraints by using the available {\it Planck} and BICEP2 datasets showing how $c_T^2$ can be measured, albeit obtaining weak constraints due to the overall poor accuracy of the current BB power spectrum measurements. The present constraint corresponds to $c_T^2 = 1.30 \pm 0.79$ and $c_T^2< 2.85$ at $95$ C.L. by assuming a power law primordial tensor power spectrum and $c_T^2<2.33$ at $95$ C.L. if the running of the spectral index is allowed. We derive forecasts for the next generation CMB satellites, which we find capable of tightly constraining $c_T^2$ at percent level, comparable with bounds from binary pulsar measurements, largely due to the absence of degeneracy with other cosmological parameters.