Lensing covariance on cut sky and SPT-Planck lensing tensions

TL;DR

This paper examines how gravitational lensing effects on incomplete sky CMB data influence tension measurements between SPT and Planck, revealing that accounting for lensing covariance reduces tension significance and hints at regional underdensity.

Contribution

It introduces a detailed analysis of lensing covariance effects on CMB data, extending methods to evaluate non-Gaussian posteriors and correlation modes, and applies these to SPT-Planck tensions.

Findings

Lensing covariance effects reduce tension significance between SPT and Planck data.

A hint of underdensity in the SPT region from super-sample lensing analysis.

Standard $A_L$ scaling underestimates tension significance when parameters are marginalized.

Abstract

We investigate correlations induced by gravitational lensing on simulated cosmic microwave background data of experiments with an incomplete sky coverage and their effect on inferences from the South Pole Telescope data. These correlations agree well with the theoretical expectations, given by the sum of super-sample and intra-sample lensing terms, with only a typically negligible $\sim$ 5% discrepancy in the amplitude of the super-sample lensing effect. Including these effects we find that lensing constraints are in $3.0\sigma$ or $2.1\sigma$ tension between the SPT polarization measurements and Planck temperature or lensing reconstruction constraints respectively. If the lensing-induced covariance effects are neglected, the significance of these tensions increases to $3.5\sigma$ or $2.5\sigma$. Using the standard scaling parameter $A_L$ substantially underestimates the significance of the tension once other parameters are marginalized over. By parameterizing the super-sample lensing through the mean convergence in the SPT footprint, we find a hint of underdensity in the SPT region. We also constrain extra sharpening of the CMB acoustic peaks due to missing smoothing of the peaks by super-sample lenses at a level that is much smaller than the lens sample variance. Finally, we extend the usual "shift in the means" statistic for evaluating tensions to non-Gaussian posteriors, generalize an approach to extract correlation modes from noisy simulated covariance matrices, and present a treatment of correlation modes not as data covariances but as auxiliary model parameters.