  The spectrum of primordial gravitational waves (GWs), especially its tilt
$n_T$, carries significant information about the primordial universe. Combining
recent aLIGO and Planck2015+BK14 data, we find that the current limit is
$n_T=0.016^{+0.614}_{-0.989}$ at 95% C.L. We also estimate the impacts of
Einstein Telescope and LISA on constraining $n_T$. Moreover, based on the
effective field theory of cosmological perturbations, we make an attempt to
confront some models of early universe scenarios, which produce blue-tilted GWs
spectrum ($n_T>0$), with the corresponding datasets.
