No evidence for the blue-tilted power spectrum of relic gravitational waves

In this paper, we constrain the tilt of the power spectrum of relic gravitational waves by combining the data from BICEP2/Keck Array and Planck (BKP) and the Laser Interferometer Gravitational-Waves Observatory (LIGO). Supposing the linearly uniform priors for both the tensor-to-scalar ratio r and the tensor tilt n_t, we find n_t=0.66^+1.83_−1.44 at the 68% confidence level from the data of BKP B-modes. By further adding the LIGO upper limit on the intensity of stochastic gravitational-wave background, the constraint becomes n_t=−0.76^+1.37_−0.52 at the 68% confidence level by assuming that the tensor amplitude has the similar order of the upper bounds from current CMB experiments. We find that there is no evidence for a blue-tilted power spectrum of relic gravitational waves and either sign of the index of tensor power spectrum is compatible with the current data.