Quantifying discordance in the 2015 Planck CMB spectrum

TL;DR

This work probes the internal consistency of the Planck 2015 TT spectrum by fitting $\Lambda\mathrm{CDM}$ parameters separately to $\ell<1000$ and $\ell\ge1000$ data, using CAMB/CosmoMC with a Planck-like $\tau$ prior and polarization-free TT likelihoods. It finds significant tension in $\Omega_ch^2$ and related parameters between the two multipole ranges, and shows that high-ℓ TT constraints are also in tension with Planck $\phi\phi$ lensing, BAO, and local $H_0$ measurements; allowing a larger lensing amplitude $A_L$ or a higher $\tau$ only partially mitigates these disagreements. The study highlights that the high-ℓ Planck TT results may reflect statistical fluctuations or unaccounted systematic effects rather than new physics, and it emphasizes caution when performing joint analyses across the full Planck multipole range. Overall, the paper argues for independent cross-checks and improved polarization and lensing data to resolve the observed tensions and robustly infer cosmology from CMB measurements.

Abstract

We examine the internal consistency of the Planck 2015 cosmic microwave background (CMB) temperature anisotropy power spectrum. We show that tension exists between cosmological constant cold dark matter (LCDM) model parameters inferred from multipoles l<1000 (roughly those accessible to Wilkinson Microwave Anisotropy Probe), and from l>=1000, particularly the CDM density, Omega_ch^2, which is discrepant at 2.5 sigma for a Planck-motivated prior on the optical depth, tau=0.07+/-0.02. We find some parameter tensions to be larger than previously reported because of inaccuracy in the code used by the Planck Collaboration to generate model spectra. The Planck l>=1000 constraints are also in tension with low-redshift data sets, including Planck's own measurement of the CMB lensing power spectrum (2.4 sigma), and the most precise baryon acoustic oscillation (BAO) scale determination (2.5 sigma). The Hubble constant predicted by Planck from l>=1000, H_0=64.1+/-1.7 km/s/Mpc, disagrees with the most precise local distance ladder measurement of 73.0+/-2.4 km/s/Mpc at the 3.0 sigma level, while the Planck value from l<1000, 69.7+/-1.7 km/s/Mpc, is consistent within 1 sigma. A discrepancy between the Planck and South Pole Telescope (SPT) high-multipole CMB spectra disfavors interpreting these tensions as evidence for new physics. We conclude that the parameters from the Planck high-multipole spectrum probably differ from the underlying values due to either an unlikely statistical fluctuation or unaccounted-for systematics persisting in the Planck data.

Figures (7)

• Figure 1: Contours enclosing 68.3% and 95.5% of MCMC sample points from fits to the Planck TT spectrum. Results are shown for $2\leq\ell<1000$, roughly the multipole range accessible to WMAP, and higher multipoles, $1000\leq\ell\leq2508$. These constraints are effectively independent and are in tension, for example $\Omega_ch^2$ differs by $2.5\sigma$. Results are also shown for the $1000\leq\ell\leq2508$ fit where the PICO code is used to estimate the theoretical TT spectra instead of the more accurate CAMB. Using PICO leads to an artificial truncation of the contours and diminishes the discrepancy between the high and low multipole fits for some parameters. We adopt a Gaussian prior of $\tau=0.07\pm0.02$.
• Figure 2: Marginalized 68.3% confidence $\Lambda\mathrm{CDM}$ parameter constraints from fits to the $\ell<1000$ and $\ell\geq1000$Planck TT spectra. Here we replace the prior on $\tau$ with fixed values of 0.06, 0.07, 0.08, and 0.09, to more clearly assess the effect $\tau$ has on other parameters in these fits. Aside from the strong correlation with $A_s$, which arises because the TT spectrum amplitude scales as $A_se^{-2\tau}$, dependence on $\tau$ is fairly weak. Tension at the $>2\sigma$ level is apparent in $\Omega_ch^2$ and derived parameters, including $H_0$, $\Omega_m$, and $\sigma_8$.
• Figure 3: Marginalized 68.3% parameter constraints from fits to the $\ell<1000$ and $\ell\geq1000$Planck TT spectra with different values of the phenomenological lensing amplitude parameter, $A_L$, which has a physical value of unity (dashed line). Increasing $A_L$ smooths out the high order acoustic peaks, which improves agreement between the two multipole ranges. Note that a high value of $A_L$ is not favored by the direct measurement of the $\phi\phi$ lensing potential power spectrum (see text).
• Figure 4: Constraints on $\sigma_8\Omega_m^{0.25}$ from fits to the $\ell<1000$ and $\ell\geq1000$ Planck TT spectra, and to the Planck $\phi\phi$ lensing spectrum. Results are shown as a function of the phenomenological lensing amplitude parameter $A_L$. The $\phi\phi$ measurement constrains the product $A_L(\sigma_8\Omega_m^{0.25})^2$. A similar trend is apparent in the $\ell\geq1000$ constraint, where lensing has a significant effect. For $\ell<1000$ the lensing effect is small, resulting in almost no dependence on $A_L$. The $\ell<1000$ and $\phi\phi$ constraints agree well for the physical value of $A_L=1$ (dashed line). Increasing $A_L$ helps reconcile the low-$\ell$ and high-$\ell$ constraints but does not improve agreement between the high-$\ell$ and $\phi\phi$ constraints.
• Figure 5: Marginalized $\Lambda\mathrm{CDM}$ parameter constraints comparing results from Planck 2015 (combined temperature, polarization and lensing) with WMAP9 alone and WMAP9 in conjunction with the Planck$\phi\phi$ lensing power spectrum. Adding the $\phi\phi$ spectrum to Planck temperature and polarization data results in a downward shift in $\tau$, which reflects internal tension between the high-multipole Planck TT spectrum and $\phi\phi$ (see text). The WMAP9 and Planck$\phi\phi$ constraints are in very good agreement. Adding $\phi\phi$ to WMAP leads to a negligible shift in $\tau$ and shifts of $<0.25\sigma$ in other parameters.