A Detailed Description of the CamSpec Likelihood Pipeline and a Reanalysis of the Planck High Frequency Maps

TL;DR

The paper presents a comprehensive, reproducible description of the CamSpec likelihood for Planck data, detailing spectra construction on masked skies, covariance modelling, and foreground treatment. By extending sky coverage up to 80% and implementing robust dust cleaning (notably using 545 GHz templates for temperature and 353 GHz for polarization), CamSpec demonstrates strong consistency of ΛCDM fits across detector sets, frequencies, and sky areas. It shows that previously discussed tensions in A_L and Ω_K can be attributed to statistical fluctuations and foreground modelling, with polarization data tightening constraints and reducing discrepancies. The work also provides a framework for evaluating extended cosmologies (A_L, Ω_K, N_eff, Σ mν, tensor amplitude) and concludes that Planck data remain remarkably compatible with ΛCDM, especially when combined with BAO and lensing information. Overall, CamSpec solidifies Planck’s role as a robust cosmological probe and offers a detailed blueprint for integrating Planck data with future ground-based CMB measurements.

Abstract

This paper presents a detailed description of the CamSpec likelihood which has been used to analyse Planck temperature and polarization maps of the cosmic microwave background since the first Planck data release. We have created a number of likelihoods using a range of Galactic sky masks and different methods of temperature foreground cleaning. Our most powerful likelihood uses 80 percent of the sky in temperature and polarization. Our results show that the six-parameter LCDM cosmology provides an excellent fit to the Planck data. There is no evidence for statistically significant internal tensions in the Planck TT, TE and EE spectra computed for different frequency combinations. We present evidence that the tendencies for the Planck temperature power spectra to favour a lensing amplitude A_L>1 and positive spatial curvature are caused by statistical fluctuations in the temperature power spectra. Using our statistically most powerful likelihood, we find that the A_L parameter differs from unity at no more than the 2.2 sigma level. We find no evidence for anomalous shifts in cosmological parameters with multipole range. In fact, we show that the combined TTTEEE likelihood over the restricted multipole range 2-800 gives cosmological parameters for the base LCDM cosmology that are very close to those derived from the full multipole range 2-2500. We present revised constraints on a few extensions of the base LCDM cosmology, focussing on the sum of neutrino masses, number of relativistic species and the tensor-scalar ratio. The results presented here show that the Planck data are remarkably consistent between detector-sets, frequencies and sky area. We find no evidence in our analysis that cosmological parameters determined from the CamSpec likelihood are affected to any significant degree by systematic errors in the Planck data (abridged).

Figures (61)

• Figure 1: TT power spectrum residuals for the CamSpec likelihood as used in PCP18 (upper figure) and for the most powerful likelihood (12.5HMcl) produced for this paper (lower figure). The residuals are computed with respect to the best-fit base $\rm{\Lambda CDM}$ cosmology and foreground model fitted to the TT spectra at $\ell\ge 30$ in combination with the low multipole temperature and polarization likelihoods at $\ell < 30$ (as discussed in Sect. \ref{['sec:Likelihood']}).
• Figure 1: Figures to the left show the sequence of apodised diffuse foreground temperature masks (from top to bottom) applied to the 217, 143 and 100 GHz maps used to form our 12.1HM likelihood. Figures to the right show the point source+CO+extended object masks that we apply to the 217, 143 and 100 GHz maps.
• Figure 1: Estimates of undeconvolved (i.e. uncorrected for missing sky and beam transfer functions) noise spectra for three half mission maps: 100 GHz HM1, 143 GHz HM2, 217 GHz HM2 computed for the masks used in the 12.1HM likelihood. The solid lines show noise estimates derived from OED maps and the dotted lines show noise estimates derived from HRD maps. T, Q, and U noise spectra are shown by the blue, red and green lines respectively. The solid black lines show the auto-spectra of the T, Q and U maps.
• Figure 1: Intra-frequency residuals for the detset $143\times 143$, $217\times217$ and $143\times 217$ TT spectra. The spectra are colour coded as follows, SWB$\times$SWB spectra are in purple, SWB$\times$PSB in green and PSB$\times$PSB in blue. $\langle D_\ell \rangle$ is the mean of the spectra within each frequency group. In each panel, the top figure shows the raw spectra, the middle figure shows the corrected spectra with multiplicative corrections $\psi_{ij}$ determined by minimising Eq. \ref{['equ:B6']} over the multipole range $50 \le \ell \le 500$, the lower figure shows results of minimisation over the multipole range $500 \le \ell \le 1000$. The panels to the left show the cross spectra as measured from the maps with no correction for correlated noise. The panels to the right show what happens if we subtract the odd-even difference spectra detset-by-detset as an indicator of correlated noise.
• Figure 1: Differences of power spectra computed on mask70 and mask50 at 857, 545 and 353 GHz scaled to match the foreground emission at 217 GHz using the cleaning coefficients given by the bold-faced entries in Table \ref{['tab:cleaning_coeffs']}. The pink points show the 'double-differenced' $217\times 217 - 143\times 143$ spectrum (renormalized to the dust amplitude of the $217 \times 217$ spectrum). The solid line shows a fit of the 545 GHz spectrum to the expression given in Eq. \ref{['equ:Noise5']}.