Analyzing weak lensing of the cosmic microwave background using the likelihood function

By C. Hirata, Uros Seljak. 2002

134 citations recorded by the source corpus.

Future experiments will produce high-resolution temperature maps of the cosmic microwave background (CMB) and are expected to reveal the signature of gravitational lensing by intervening large-scale structures. We construct all-sky maximum-likelihood estimators that use the lensing effect to estimate the projected density (convergence) of these structures, its power spectrum, and cross-correlation with other observables. This contrasts with earlier quadratic-estimator approaches that Taylor expanded the observed CMB temperature to linear order in the lensing deflection angle; these approaches gave estimators for the temperature-convergence correlation in terms of the CMB three-point correlation function and for the convergence power spectrum in terms of the CMB four-point correlation function, which can be biased and nonoptimal due to terms beyond the linear order. We show that for sufficiently weak lensing, the maximum-likelihood estimator reduces to the computationally less demanding quadratic estimator. The maximum likelihood and quadratic approaches are compared by evaluating the root-mean-square (rms) error and bias in the reconstructed convergence map in a numerical simulation; it is found that both the rms errors and bias are of order 1 percent for the case of Planck and of order 10–20 percent for a 1 arcminute beam experiment. We conclude that for recovering lensing information from temperature data acquired by these experiments, the quadratic estimator is close to optimal, but further work will be required to determine whether this is also the case for lensing of the CMB polarization field.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/27213e0cde0468001f6a7be5fe54fd80c81ce416

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Astronomy and Astrophysics

Citations in the corpus

Galaxy Bias and non-Linear Structure Formation in General Relativity (2011, unknown): “One could also use the anisotropies in the small scale power to de-lense the CMB along the lines considered in [37, 38].”
SIMULATIONS OF THE MICROWAVE SKY (2009, background): “By studying the lensing distortions in the microwave sky, we should also be able to reconstruct the projected matter distribution or the deflection field in the Universe (Hu & Okamoto 2002; Okamoto & Hu 2003; Hirata & Seljak 2003; Yoo & Zaldarriaga 2008).”
A MEASUREMENT OF GRAVITATIONAL LENSING OF THE MICROWAVE BACKGROUND USING SOUTH POLE TELESCOPE DATA (2012, methodology): “Alternative approaches involve formulating and maximizing a lensing likelihood function in pixel space (Hirata & Seljak 2003a,b; Anderes et al. 2011).”
Gravitational lensing (2010, methodology): “Distortions of the probability distribution function of CMB temperature fluctuations, higher order correlations, quadratic filtering and maximumlikelihood approaches were developed to identify lensing in the CMB at the statistical level and in two-dimensional reconstructions [164, 193, 194, 212, 246”
Observational probes of cosmic acceleration (2012, methodology): “Pan-STARRS and DES will both carry out large area, multi-band imaging surveys that go a factor of ten or more deeper (in flux) than the SDSS imaging survey (Abazajian et al., 2009), using, respectively, a 1.4-Gigapixel camera on the 1.8-m PS1 telescope on Haleakala in Hawaii and a 0.5-Gigapixel came”
Delensing CMB polarization with external datasets (2010, background): “2 Temperature delensing Lens reconstruction estimators can also be used to estimate the lensing potential from CMB temperature measurements which extend to small angular scales [35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45].”