  We study the tilt of the primordial gravitational waves spectrum. A hint of
blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by
this, we explore the possibilities of blue tensor spectra from the very early
universe cosmology models, including null energy condition violating inflation,
inflation with general initial conditions, and string gas cosmology, etc. For
the simplest G-inflation, blue tensor spectrum also implies blue scalar
spectrum. In general, the inflation models with blue tensor spectra indicate
large non-Gaussianities. On the other hand, string gas cosmology predicts blue
tensor spectrum with highly Gaussian fluctuations. If further experiments do
confirm the blue tensor spectrum, non-Gaussianity becomes a distinguishing test
between inflation and alternatives.
