  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.

Cosmology and Nongalactic Astrophysics