Planck constraints on the tensor-to-scalar ratio

TL;DR

This paper uses Planck data to constrain the tensor-to-scalar ratio r, providing tighter limits through polarization and temperature spectra analysis, and combining with other datasets, to inform models of cosmic inflation.

Contribution

First comprehensive analysis of Planck PR4 data constraining r using polarization BB spectrum, improving limits and consistency checks with temperature data and external experiments.

Findings

Planck BB spectrum constrains r<0.069 at 95% confidence.

Combined Planck data yields r<0.056, tighter than previous limits.

Including BICEP2/Keck data further tightens the constraint to r<0.044.

Abstract

We present constraints on the tensor-to-scalar ratio r using Planck data. We use the latest release of Planck maps (PR4), processed with the NPIPE code, which produces calibrated frequency maps in temperature and polarization 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 marginalized 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 'reionization bump') and intermediate angular scales (the 'recombination bump') from $\ell$=2 to 150, and find a stronger constraint than that from TT, with $\sigma$(r)=0.069. The Planck BB 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 Planck EE, BB, and EB power spectra are combined consistently, and it tightens further to r<0.056 when the Planck TT power spectrum is included in the combination. Finally, combining Planck with BICEP2/Keck 2015 data yields an upper limit of r<0.044.