  A primordial gravitational wave background with positive(blue) spectral index
is expected in several non-standard inflationary cosmologies where the
stress-energy tensor violates the null energy condition. Here we show that a
sizable amount of blue gravitational waves is compatible with current
cosmological and astrophysical data. So far most of the works on parameter
estimation from cosmic microwave background data have assumed a negative or
negligible spectral index. The present limits on cosmological parameters,
especially on the scalar spectral index, widen up considerably when one allows
also for blue tilts of the tensor spectrum. Since the amplitude of the CMB
B-mode polarization is larger in these models, future data from Planck are
likely to provide crucial measurements.
