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

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.

The XFaster Power Spectrum and Likelihood Estimator for the Analysis of Cosmic Microwave Background Maps

We present the XFaster analysis package, a fast, iterative angular power spectrum estimator based on a diagonal approximation to the quadratic Fisher matrix estimator. It uses Monte Carlo simulations to compute noise biases and filter transfer functions and is thus a hybrid of both Monte Carlo and quadratic estimator methods. In contrast to conventional pseudo-C ℓ –based methods, the algorithm described here requires a minimal number of simulations and does not require them to be precisely representative of the data to estimate accurate covariance matrices for the bandpowers. The formalism works with polarization-sensitive observations and also data sets with identical, partially overlapping, or independent survey regions. The method was first implemented for the analysis of BOOMERanG data and also used as part of the Planck analysis. Here we describe the full, publicly available analysis package, written in Python, as developed for the analysis of data from the 2015 flight of the Spider instrument. The package includes extensions for self-consistently estimating null spectra and estimating fits for Galactic foreground contributions. We show results from the extensive validation of XFaster using simulations and its application to the Spider data set.

Gaussian process foreground subtraction and power spectrum estimation for 21 cm cosmology

ABSTRACT One of the primary challenges in enabling the scientific potential of 21 cm intensity mapping at the epoch of reionization (EoR) is the separation of astrophysical foreground contamination. Recent works have claimed that Gaussian process regression (GPR) can robustly perform this separation, particularly at low Fourier k wavenumbers where the EoR signal reaches its peak signal-to-noise ratio. We revisit this topic by casting GPR foreground subtraction (GPR-FS) into the quadratic estimator formalism, thereby putting its statistical properties on stronger theoretical footing. We find that GPR-FS can distort the window functions at these low k modes, which, without proper decorrelation, make it difficult to probe the EoR power spectrum. Incidentally, we also show that GPR-FS is in fact closely related to the widely studied inverse covariance weighting of the optimal quadratic estimator. As a case study, we look at recent power spectrum upper limits from the Low-Frequency Array (LOFAR) that utilized GPR-FS. We pay close attention to their normalization scheme, showing that it is particularly sensitive to signal loss when the EoR covariance is misestimated. This has possible ramifications for recent astrophysical interpretations of the LOFAR limits, because many of the EoR models ruled out do not fall within the bounds of the covariance models explored by LOFAR. Being more robust to this bias, we conclude that the quadratic estimator is a more natural framework for implementing GPR-FS and computing the 21 cm power spectrum.

Optimal 1D Ly α forest power spectrum estimation – I. DESI-lite spectra

ABSTRACT The 1D Ly α forest flux power spectrum P1D is sensitive to scales smaller than a typical galaxy survey, and hence ties to the intergalactic medium’s thermal state, suppression from neutrino masses, and new dark matter models. It has emerged as a competitive framework to study new physics, but also has come with various challenges and systematic errors in analysis. In this work, we revisit the optimal quadratic estimator for P1D, which is robust against the relevant problems such as pixel masking, time evolution within spectrum, and quasar continuum errors. We further improve the estimator by introducing a fiducial power spectrum, which enables us to extract more information by alleviating the discreteness of band powers. We meticulously apply our method to synthetic Dark Energy Spectroscopic Instrument (DESI) spectra and demonstrate how the estimator overcomes each challenge. We further apply an optimization scheme that approximates the Fisher matrix to three elements per row and reduces computation time by 60 per cent. We show that we can achieve per cent precision in P1D with 5-yr DESI data in the absence of systematics and provide forecasts for different spectral qualities.

Reconstructing small-scale lenses from the cosmic microwave background temperature fluctuations

Cosmic microwave background (CMB) lensing is a powerful probe of the matter distribution in the Universe. The standard quadratic estimator, which is typically used to measure the lensing signal, is known to be suboptimal for low-noise polarization data from next-generation experiments. In this paper, we explain why the quadratic estimator will also be suboptimal for measuring lensing on very small scales, even for measurements in temperature where this estimator typically performs well. Though maximum likelihood methods could be implemented to improve performance, we explore a much simpler solution, revisiting a previously proposed method to measure lensing that involves a direct inversion of the background gradient. An important application of this simple formalism is the measurement of cluster masses with CMB lensing. We find that directly applying a gradient inversion matched filter to simulated lensed images of the CMB can tighten constraints on cluster masses compared to the quadratic estimator. While the difference is not relevant for existing surveys, for future surveys it can translate to significant improvements in mass calibration for distant clusters, where galaxy lensing calibration is ineffective due to the lack of enough resolved background galaxies. Improvements can be as large as ${\sim } 50{{\ \rm per\ cent}}$ for a cluster at z = 2 and a next-generation CMB experiment with 1 $\mu$K arcmin noise, and over an order of magnitude for lower noise levels. For future surveys, this simple matched filter or gradient inversion method approaches the performance of maximum likelihood methods, at a fraction of the computational cost.