Mapping the Dark Matter through the CMB Damping Tail

TL;DR

The paper addresses mapping dark matter via gravitational lensing of the CMB, focusing on the damping tail where lensing effects are enhanced. It introduces a quadratic estimator based on four-point information to reconstruct a projected mass map from high-resolution, low-foreground CMB data, and outlines a Fourier-domain gradient-based reconstruction pipeline with proper normalization and bias handling. The authors provide forecasts showing high signal-to-noise for large-scale mass structures under realistic instrument specifications (beam < 5' and noise around 15 (10^-6-arcmin) or 41 μK-arcmin) and demonstrate robust recovery in simulations. This work offers a practical route to map dark matter in projection on degree scales, enabling cross-correlations with secondary anisotropies and complementing traditional weak lensing surveys.

Abstract

The lensing of CMB photons by intervening large-scale structure leaves a characteristic imprint on its arcminute-scale anisotropy that can be used to map the dark matter distribution in projection on degree scales or ~100 Mpc/h comoving. We introduce a new algorithm for mass reconstruction which optimally utilizes information from the weak lensing of CMB anisotropies in the damping tail. It can ultimately map individual degree scale mass structures with high signal-to-noise. To achieve this limit an experiment must produce a high signal-to-noise, foreground-free CMB map of arcminute scale resolution, specifically with a FWHM beam of < 5' and a noise level of < 15 (10^-6-arcmin) or 41 (uK-arcmin).

Figures (4)

• Figure 1: Lensing deflection power spectrum for the $\Lambda$CDM model. Error bars represent the total (sample plus noise) variance and sample variance from recovery from an area of $f_{\rm sky}=0.1$ and an experiment with a beam of $\sigma=1.5'$ and noise $w^{-1/2}=10$$(10^{-6}$-arcmin). Note that the errors for $L \lesssim 200$ are dominated by sample variance implying that the recovered map has high signal-to-noise.
• Figure 2: Top: A $32^\circ \times 32^\circ$ realization of the CMB temperature field. Bottom: A toy example of the lensing effect. A circularly symmetric projected mass with deflection angles comparable to the size of the structure. The distortion of the fine-scale anisotropy of the CMB traces the lensing structure on much larger scales.
• Figure 3: Top: A $32^\circ \times 32^\circ$ realization of the deflection field in the $\Lambda$CDM model. Bottom: Recovery of the deflection field with a $\sigma=1.5'$ beam (FWHM) and detector noise of $w^{-1/2} = 10$$(10^{-6}$-arcmin).
• Figure 4: Signal-to-noise as a function of detector noise, beam and sky fraction $f_{\rm sky}$. Solid lines include both sample and Gaussian noise (primary CMB and instrumental) variance; dashed lines include only Gaussian noise variance. The signal-to-noise drops off rapidly for $w^{-1/2}>15$$(10^{-6}$-arcmin) and FWHM beams $\sigma>5'$.