Mass Reconstruction with CMB Polarization

TL;DR

Mass Reconstruction with CMB Polarization shows how weak lensing induces mode coupling in the CMB, enabling mass mapping via minimum-variance quadratic estimators that exploit polarization, especially the EB pair. The work demonstrates polarization-based estimators can achieve cosmic-variance-limited mass maps up to L ~ 1000, far surpassing temperature-only methods, and outlines applications to the projected matter power spectrum, tomographic structure growth, dark energy via ISW cross-correlations, and separation of lensing from primordial B-modes. It highlights the practical advantages and challenges of deploying sensitive polarization experiments for high-fidelity mass reconstruction and lensing decontamination. Overall, polarization-based mass reconstruction offers a powerful, complementary probe of cosmology across a wide range of scales and epochs.

Abstract

Weak gravitational lensing by the intervening large-scale structure of the Universe induces high-order correlations in the cosmic microwave background (CMB) temperature and polarization fields. We construct minimum variance estimators of the intervening mass distribution out of the six quadratic combinations of the temperature and polarization fields. Polarization begins to assist in the reconstruction when E-mode mapping becomes possible on degree-scale fields, i.e. for an experiment with a noise level of ~40 uK-arcmin and beam of ~7', similar to the Planck experiment; surpasses the temperature reconstruction at ~26 uK-arcmin and 4'; yet continues to improve the reconstruction until the lensing B-modes are mapped to l ~ 2000 at ~0.3 uK-arcmin and 3'. Ultimately, the correlation between the E and B modes can provide a high signal-to-noise mass map out to multipoles of L ~ 1000, extending the range of temperature-based estimators by nearly an order of magnitude. We outline four applications of mass reconstruction: measurement of the linear power spectrum in projection to the cosmic variance limit out to L ~ 1000 (or wavenumbers 0.002 < k < 0.2 in h/Mpc), cross-correlation with cosmic shear surveys to probe the evolution of structure tomographically, cross-correlation of the mass and temperature maps to probe the dark energy, and the separation of lensing and gravitational wave B-modes.

Figures (9)

• Figure 1: An exaggerated example of the lensing effect on a $10^\circ \times 10^\circ$ field. Top: (left-to-right) unlensed temperature field, unlensed $E$-polarization field, spherically symmetric deflection field $d(\bf n)$. Bottom: (left-to-right) lensed temperature field, lensed $E$-polarization field, lensed $B$-polarization field. The scale for the polarization and temperature fields differ by a factor of 10.
• Figure 2: Power spectra of the CMB temperature and polarization fields compared with the detector noise of the Planck satellite and a nearly perfect experiment with a noise level of $\Delta_T = \Delta_P/\sqrt{2}= 1 \mu$K-arcmin and a beam of $\sigma=4'$ (long dashed lines, thick for polarization, thin for temperature). The Planck experiment has sufficient signal-to-noise to map the $\Theta$ field but can only marginally map the $E$-polarization field; the nearly perfect experiment can map the all three fields to $l = 2000$.
• Figure 3: Deflection signal ($dd$) and noise power spectra of the quadratic estimators and their minimum variance (mv) combination: (a) Planck experiment (b) reference experiment. As the sensitivity of the experiment improves the best quadratic estimator switches from $\Theta\Theta$ to $EB$. Only the $EB$-estimator can reconstruct the mass distribution at $L \gtrsim 200$.
• Figure 4: Deflection signal ($dd$) and noise power spectra for the minimum variance (mv; solid lines) and $\Theta\Theta$ (dashed lines) estimators as a function of (a) beam size $\sigma$ and (b) noise level $\Delta_T=\Delta_P/\sqrt{2}$. The noise saturates to its minimum by $\sigma \approx 2-4'$ and $\Delta_T \approx 0.1-0.3 \mu$K-arcmin as the polarization field is mapped to the cosmic variance limit out to $l < 2000$.
• Figure 5: Mass reconstruction on a $10^\circ \times 10^\circ$ field with the reference experiment ($\Delta_T=\Delta_P/\sqrt{2}=1 \mu$K-arcmin and $\sigma=4'$): (a) deflection field, (b) $\Theta\Theta$-reconstruction, (c) $EB$-reconstruction.