Abstract
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 σr = 0.093), but we show that the marginalised posterior peaks towards negative values of r at about the 1.2σ 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 σr = 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.
Highlights
As described in Planck Collaboration VI (2020) and Planck Collaboration X (2020), the comoving wavenumbers of tensor modes probed by the cosmic microwave background (CMB) temperature anisotropy power spectrum have k 0.008 Mpc−1, with very little sensitivity to higher wavenumbers because gravitational waves decay on sub-horizon scales
These measurements probe the peak of the Bmode power spectrum at around = 100, corresponding to gravitational waves with k ≈ 0.01 Mpc−1 that enter the horizon during recombination
When regressing the templates fitted during the map-making process with pure E and B CMB maps, we found a similar impact on the EE and BB power spectra
Summary
While the idea of cosmic inflation was introduced about 40 years ago to solve inherent problems with the canonical hot bigbang model (Brout et al 1978; Starobinsky 1980; Kazanas 1980; Sato 1981; Guth 1981; Linde 1982, 1983; Albrecht & Steinhardt 1982), attention quickly focused on using it as a means to generate cosmological perturbations from quantum fluctuations (Mukhanov & Chibisov 1981, 1982; Hawking 1982; Guth & Pi 1982; Starobinsky 1982; Bardeen et al 1983; Mukhanov 1985). At present the tightest B-mode constraints on r come from the BICEP/Keck measurements (BK15; BICEP2 Collaboration 2018), which cover approximately 400 deg centred on RA = 0h, Dec = −57◦.5 These measurements probe the peak of the Bmode power spectrum at around = 100, corresponding to gravitational waves with k ≈ 0.01 Mpc−1 that enter the horizon during recombination (i.e. somewhat smaller than the scales contributing to the Planck temperature constraints on r). Planck Collaboration VI 2020) In this model, we assume purely adiabatic, nearly scale-invariant perturbations at very early times, with curvature-mode (scalar) and tensor-mode power spectra parameterised by. We use 95% confidence levels when reporting upper limits, and a 68% confidence interval with the maximum a posteriori probability
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