The Tilt of Primordial Gravitational Waves Spectra from BICEP2

In this paper we constrain the tilt of the spectra of primordial gravitational waves from Background Imaging of Cosmic Extragalactic Polarization (BICEP2) data only. We find $r=0.21_{-0.10}^{+0.04}$ and $n_t=-0.06_{-0.23}^{+0.25}$ (at $68\%$ C.L.) which implies that a scale-invariant primordial gravitational waves spectra is consistent with BICEP2 nicely. Our results provide strong evidence for supporting inflation model, and the alternative models, for example the ekpyrotic model which predicts $n_t=2$, are ruled out at more than $5\sigma$ significance.