Optimal Cosmic Microwave Background Lensing Reconstruction and Parameter Estimation with SPTpol Data

Abstract

We perform the first simultaneous Bayesian parameter inference and optimal reconstruction of the gravitational lensing of the cosmic microwave background (CMB), using 100 deg2 of polarization observations from the SPTpol receiver on the South Pole Telescope. These data reach noise levels as low as 5.8 μK arcmin in polarization, which are low enough that the typically used quadratic estimator (QE) technique for analyzing CMB lensing is significantly suboptimal. Conversely, the Bayesian procedure extracts all lensing information from the data and is optimal at any noise level. We infer the amplitude of the gravitational lensing potential to be A ϕ = 0.949 ± 0.122 using the Bayesian pipeline, consistent with our QE pipeline result, but with 17% smaller error bars. The Bayesian analysis also provides a simple way to account for systematic uncertainties, performing a similar job as frequentist “bias hardening” or linear bias correction, and reducing the systematic uncertainty on A ϕ due to polarization calibration from almost half of the statistical error to effectively zero. Finally, we jointly constrain A ϕ along with A L, the amplitude of lensing-like effects on the CMB power spectra, demonstrating that the Bayesian method can be used to easily infer parameters both from an optimal lensing reconstruction and from the delensed CMB, while exactly accounting for the correlation between the two. These results demonstrate the feasibility of the Bayesian approach on real data, and pave the way for future analysis of deep CMB polarization measurements with SPT-3G, Simons Observatory, and CMB-S4, where improvements relative to the QE can reach 1.5 times tighter constraints on A ϕ and seven times lower effective lensing reconstruction noise.

Normalizing flows for random fields in cosmology

“…We have considered relatively small 2-dimensional maps here, up to a side length of 128 pixels. In practice, analysing a small but very deep sky patch with HMC such as for CMB lensing in [12] could benefit from a non-Gaussian prior distribution of the lensing potential represented with a normalizing flow. We are in particular interested in applying flows to kinetic Sunyaev-Zeldovich tomography [23,24], where the scales that generate the kSZ signal are highly non-linear.…”

“…Normalizing flows are ideally suited for variational inference [4]. In our lensing potential example, this would mean to make a variational estimate of the lensing potential rather than a MAP as in [11] or an HMC sampling as in [12]. Hamiltonial Variational Inference [13] may also be useful for this purpose.…”

Primordial Power Spectrum from Lensed CMB Temperature Spectrum using Iterative Delensing

“…There have been purported anomalies in recent cosmological results, some of which are statistically significant, such as the Hubble constant discrepancy from the ΛCDM standard model validating using Planck data [32][33][34][35], which now stands at a 4.4σ deviation [1,17]. Some of such anomalies are less clear as to if they are statistical artefacts, or actual observational outliers, such as the A L anomaly, where deviations from the theoretical smoothing of the weak lensing of CMB power spectra shows a 10% excess, albeit at only 2σ deviation [2,3,33]. Ironically, the theoretical framework of weak lensing, under General Relativity, is highly quantified and well established by a plethora of independent and diverse observational data.…”

BICEP / Keck XVII: Line of Sight Distortion Analysis: Estimates of Gravitational Lensing, Anisotropic Cosmic Birefringence, Patchy Reionization, and Systematic Errors

“…The (gradient) CMB lensing potential power spectrum has been measured to high precision by many experiments using temperature, polarization, or both (van Engelen et al (2012); Sherwin et al (2017); Planck Collaboration et al (2020a); Carron et al (2022); Faúndez et al (2020); Wu et al (2019); Millea et al (2021); BK-VIII).…”