We present new constraints on the spectral index n_T of tensor fluctuations from the recent data obtained by the BICEP2 experiment. We found that the BICEP2 data alone slightly prefers a positive, "blue", spectral index with n_T=1.36\pm0.83 at 68 % c.l.. However, when a TT prior on the tensor amplitude coming from temperature anisotropy measurements is assumed we get n_T=1.67\pm0.53 at 68 % c.l., ruling out a scale invariant $n_T=0$ spectrum at more than three standard deviations. These results are at odds with current bounds on the tensor spectral index coming from pulsar timing, Big Bang Nucleosynthesis, and direct measurements from the LIGO experiment. Considering only the possibility of a "red", n_T<0 spectral index we obtain the lower limit n_T > -0.76 at 68 % c.l. (n_T>-0.09 when a TT prior is included).

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