Cross-correlation of CMB with large-scale structure: weak gravitational lensing

TL;DR

This paper conducts a first-principles cross-correlation search for weak gravitational lensing of the CMB by large-scale structure, using WMAP year-1 temperature maps and SDSS LRGs. It reconstructs a CMB lensing field with a quadratic estimator, then cross-correlates it with the LRG density to infer the galaxy bias $b_g$; despite meticulous treatment of masks, beam effects, and foregrounds, no significant lensing signal is detected, yielding $b_g=1.81\pm1.92$. The work rigorously evaluates systematic errors, finding Galactic foregrounds negligible but extragalactic foregrounds (notably point sources and tSZ) to be potential contaminants given the current data quality and frequency coverage. The study establishes a robust framework for future, higher-sensitivity lensing analyses with broader frequency data (e.g., Planck), and highlights the importance of foreground control in CMB-lensing cross-correlation studies. Overall, it confirms the feasibility of CMB-lensing cross-correlation while underscoring the need for improved data to achieve a detection and precise cosmological constraints.

Abstract

We present the results of a search for gravitational lensing of the cosmic microwave background (CMB) in cross-correlation with the projected density of luminous red galaxies (LRGs). The CMB lensing reconstruction is performed using the first year of Wilkinson Microwave Anisotropy Probe (WMAP) data, and the galaxy maps are obtained using the Sloan Digital Sky Survey (SDSS) imaging data. We find no detection of lensing; our constraint on the galaxy bias derived from the galaxy-convergence cross-spectrum is $b_g=1.81\pm 1.92$ ($1σ$, statistical), as compared to the expected result of $b_g\sim 1.8$ for this sample. We discuss possible instrument-related systematic errors and show that the Galactic foregrounds are not important. We do not find any evidence for point source or thermal Sunyaev-Zel'dovich effect contamination.

Figures (13)

• Figure 1: The LRG redshift distribution. The black histogram shows the photo-$z$ distribution, the red curve is the true redshift distribution estimated by regularized deconvolution of the photo-$z$ errors.
• Figure 2: The response factor $R_l$ of Eq. (\ref{['eq:calib']}) satisfying $\langle v^{\alpha\beta(\parallel)}_{lm}\rangle = R_l\kappa_{lm}$.
• Figure 3: (a) The weight functions $W_l$ and $C_lW_l$. (b) The same weight functions in real-space (Eq. \ref{['eq:real']}); $W\hat{T}$ and $CW\hat{T}$ are obtained by convolving the (beam-deconvolved) temperature $\hat{T}$ with these kernels.
• Figure 4: The divergence of the lensing vector field map, $\nabla\cdot{\bf v}^{(TT)}$, smoothed with a 30 arcmin FWHM Gaussian, and displayed in Galactic Molleweide projection. Note the prominent artifacts surrounding the Galactic plane cut and the point sources (which are removed by the Kp05$\cap$S10$\setminus$ps$_2$ cut).
• Figure 5: The longitudinal mode power spectrum $C_{l,\parallel}^{vv}$ within the Kp05$\cap$S10$\setminus$ps$_2$ cut (solid line), for each of the six frequency pairs. The points show 10 simulations (containing no lensing or foregrounds). Since the purpose of this plot is to compare the simulations to the actual data, the sky cut has not been deconvolved, rather we have plotted the average of $|\int {\bf v}\cdot{\bf Y}^{(\parallel)\ast}_{lm} d^2\hat{\bf n}/f_{sky}|^2$ within bands of width $\Delta l=10$.