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

Abstract: 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). From the data of BKP B-modes, the constraint on the tensor tilt is $n_t=0.66^{+1.83}_{-1.44}$ at the $68%$ confidence level. By further adding the LIGO upper limit on the energy density of gravitational waves, the constraint becomes $n_t=-0.76^{+1.37}_{-0.52}$ at the $68%$ confidence level. We conclude 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 data.