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

TL;DR

This study combines data from multiple gravitational wave observations to constrain the tilt of the relic gravitational wave spectrum, finding no evidence for a blue tilt and showing both signs of the tensor spectral index are compatible with current data.

Contribution

It provides the first combined constraints on the tensor tilt using BICEP2/Keck, Planck, and LIGO data, clarifying the spectrum's tilt is not definitively blue or red.

Findings

No evidence for a blue-tilted tensor spectrum

Tensor tilt constraints are consistent with zero within uncertainties

Both positive and negative tilt values are compatible with observations

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.