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 investigate the effects of a modified speed of gravity, $c_T^2$, on the $B$ modes of the cosmic microwave background (CMB) anisotropy in polarization. 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 which allows us to constrain $c_T$ without any significant degeneracy with other cosmological parameters. We derive constraints from current data and forecast the accuracy with which $c_T$ will be measured by the next generation CMB satellites. In the former case, using the available Planck and BICEP2 data sets, we obtain $c_T^2=1.30\pm 0.79$ 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. More interestingly, in the latter case we find future CMB satellites capable of 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.

Figure 1

(Left panel) The total $B$-mode polarization power spectrum (solid lines) and its component due to tensor perturbations (dashed lines). (Right panel) The total CMB temperature power spectrum (solid lines) and its tensor component (dashed lines). In both panels different colors correspond to different values of the speed of the GWs. The other cosmological parameters are fixed to the best fit of the Planck and BICEP2 data sets.

Figure 2

(Left panels) The marginalized joint likelihood for the GWs speed of sound $c_T^2$ and parameters defining the primordial tensor power spectrum: the tensor to scalar ratio $r_{0.002}$, the scalar perturbation spectral index $n_s$, and its running $d{n}_s/d\text{ln}k$. Different colors correspond to different combinations of data sets and models, as shown in the legend. The two different shades indicate the 68% and 95% confidence regions. (Right panels) Marginalized likelihoods of the tensor perturbation sound speed for the considered data sets and models.

Figure 3

The marginalized joint likelihood for the GW’s speed of sound $c_T^2$, the tensor to scalar ratio $r_{0.002}$, the scalar perturbation spectral index $n_s$, and its running $d{n}_s/d\text{ln}k$. Different colors correspond to different instrumental specifications used in the forecast and different models, as shown in the legend. The two different shades indicate the 68% and 95% confidence regions.