Planck constraints on the tensor-to-scalar ratio

We present constraints on the tensor-to-scalar ratio r using Planck data. We use the latest release of Planck maps, processed with the NPIPE code, which produces calibrated frequency maps in temperature and polarisation for all Planck channels from 30 GHz to 857 GHz using the same pipeline. We computed constraints on r using the BB angular power spectrum, and we also discuss constraints coming from the TT spectrum. Given Planck's noise level, the TT spectrum gives constraints on r that are cosmic-variance limited (with sigma (r)=0.093), but we show that the marginalised posterior peaks towards negative values of r at about the 1.2 sigma level. We derived Planck constraints using the BB power spectrum at both large angular scales (the 'reionisation bump') and intermediate angular scales (the 'recombination bump') from l = 2 to 150 and find a stronger constraint than that from TT, with sigma (r)=0.069. The PlanckBB spectrum shows no systematic bias and is compatible with zero, given both the statistical noise and the systematic uncertainties. The likelihood analysis using B modes yields the constraint r<0.158 at 95% confidence using more than 50% of the sky. This upper limit tightens to r<0.069 when PlanckEE, BB, and EB power spectra are combined consistently, and it tightens further to r<0.056 when the PlanckTT power spectrum is included in the combination. Finally, combining Planck with BICEP2/Keck 2015 data yields an upper limit of r<0.044.

Automated summary

The study presents constraints on the tensor-to-scalar ratio r using Planck data, with results indicating a stronger constraint on r through the BB angular power spectrum compared to the TT spectrum. The combination of Planck with BICEP2/Keck 2015 data yields an upper limit of r<0.044, demonstrating the accuracy and significance of the constraints obtained.