Multi-wavelength constraints on the inflationary consistency relation

We present the first attempt to use a combination of CMB, LIGO, and PPTA data to constrain both the tilt and the running of primordial tensor power spectrum through constraints on the gravitational wave energy density generated in the early universe. Combining measurements at different cosmological scales highlights how complementary data can be used to test the predictions of early universe models including the inflationary consistency relation. Current data prefers a slightly positive tilt ($n_t = 0.06^{+0.63}_{-0.89}$) and a negative running ($n_{t, {\rm run}} < -0.22$) for the tensor power spectrum spectrum. Interestingly, the addition of direct gravitational wave detector data alone puts strong bounds on the tensor-to-scalar ratio $r < 0.2$ since the large positive tensor tilt preferred by the \textit{Planck} temperature power spectrum is no longer allowed. Adding the recently released BICEP2/KECK and Planck 353 GHz Polarization cross correlation data puts an even stronger bound $r<0.1$ . We comment on possible effects of a large positive tilt on the background expansion and show that depending on the assumptions regarding the UV cutoff ($k_{\rm UV}/k_* = 10^{24}$) of the primordial spectrum of gravitational waves, the strongest bounds on $n_t = 0.07^{+0.52}_{-0.80}$ are derived from this effect.