Weak Gravitational Lensing of the CMB

TL;DR

Weak gravitational lensing of the CMB induces non-Gaussian signatures (bispectrum and trispectrum) and generates B-mode polarization by distorting primary fluctuations, which in turn informs both fundamental physics and cosmological parameters. The paper outlines theoretical derivations of non-Gaussian signals, practical estimators (temperature and polarization quadratic estimators) and Bayesian approaches for reconstructing the lensing potential, and discusses delensing strategies. It covers observational status, implications for dark energy, neutrino masses, and cluster masses, and highlights the need to incorporate lensing non-Gaussianity in high-precision analyses. Overall, CMB lensing provides a robust, multi-faceted probe of late-time structure and cosmology, with significant implications for future high-resolution, low-noise polarization measurements and delensing efforts.

Abstract

Weak gravitational lensing has several important effects on the cosmic microwave background (CMB): it changes the CMB power spectra, induces non-Gaussianities, and generates a B-mode polarization signal that is an important source of confusion for the signal from primordial gravitational waves. The lensing signal can also be used to help constrain cosmological parameters and lensing mass distributions. We review the origin and calculation of these effects. Topics include: lensing in General Relativity, the lensing potential, lensed temperature and polarization power spectra, implications for constraining inflation, non-Gaussian structure, reconstruction of the lensing potential, delensing, sky curvature corrections, simulations, cosmological parameter estimation, cluster mass reconstruction, and moving lenses/dipole lensing.

Figures (5)

• Figure 15: A simulated reconstruction of the magnitude of the deflection angle from Ref. Hu:2001kj. The left panel shows the deflection from the realization used in the simulation. The centre panel shows the field reconstructed using the temperature quadratic estimator. The right hand panel shows the better result from using the $EB$ quadratic estimator. The simulation is for an idealized CMB observation with isotropic white-noise variance $N_l^\Theta=N^E_{l}/2=N^B_{l}/2 = 8.5\times 10^{-8} \mu\rm{K}^2$ ($\surd{N_l^\Theta} = 1 \mu\rm{K}$-arcmin) and beam full-width half-maximum of $4\,\text{arcmin}$. The frames are $10^\circ\times 10^\circ$.
• Figure 16: A simulated reconstruction of the lensing convergence $\kappa$ from Ref. Hirata:2003ka using CMB polarization. The left panel shows a realization of the convergence used in the simulation. The centre panel shows the Wiener filtered field reconstructed using the quadratic estimator. The right hand panel shows the improved iterative Bayesian estimator of Ref. Hirata:2003ka. The simulation is for an idealized CMB observation with isotropic white-noise variance $N^E_{l}=N^B_{l} = 1.7\times 10^{-7} \mu\rm{K}^2$ ($\surd N^E_l = 1.41\mu\rm{K}\,\text{arcmin}$, about $50$ times lower than Planck) and beam full-width half-maximum of $4\, \mu$K-arcmin. The frames are $8^\circ 32'$ in width, and show only the $l\le1600$ modes for clarity. The Wiener filtered field appears smoother because the filtering suppresses the poorly recovered small-scale modes.
• Figure 17: The fractional difference between the lensed CMB power spectra using the flat-sky approximation compared to the full-sky method (using the second-order result given in Ref. Challinor:2005jy).
• Figure 18: Effect on lensing potential power spectrum (top) and lensed CMB spectra (bottom) of varying the neutrino mass (assumed the same for all three families) and equation of state of dark energy at fixed angular diameter distance to last scattering in a flat model. The error boxes are cosmic variance errors and ignore non-Gaussianity for the lensed CMB spectra.
• Figure 19: Simulated effect of cluster lensing on the CMB temperature. Left: the unlensed CMB; middle: the lensed CMB; right: the difference due to the cluster lensing. The cluster is at redshift one, and has a spherically symmetric NFW profile with mass of $m_{200} = 10^{15} h^{-1} M_\odot$ and concentration parameter $c=5$ (see Refs. Dodelson:2004asLewis:2005fq). Distances are in arcminutes, and can be compared to the cluster virial radius of $3.3\,\text{arcmin}$. In the middle figure note the direction of the gradient inverts inside the $\sim 1\,\text{arcmin}$ Einstein radius where the lensing deflections cross the centre of the cluster. This is a rather clean realization, in general the dipole pattern can be weaker and/or more complicated.