The shape of the CMB lensing bispectrum
Abstract
Lensing of the CMB generates a significant bispectrum, which should be detected by the Planck satellite at the 5sigma level and is potentially a nonnegligible source of bias for f_{NL} estimators of local nonGaussianity. We extend current understanding of the lensing bispectrum in several directions: (1) we perform a nonperturbative calculation of the lensing bispectrum which is ~ 10% more accurate than previous, firstorder calculations; (2) we demonstrate how to incorporate the signal variance of the lensing bispectrum into estimates of its amplitude, providing a good analytical explanation for previous MonteCarlo results; and (3) we discover the existence of a significant lensing bispectrum in polarization, due to a previouslyunnoticed correlation between the lensing potential and Epolarization as large as 30% at low multipoles. We use this improved understanding of the lensing bispectra to reevaluate Fishermatrix predictions, both for Planck and cosmic variance limited data. We confirm that the nonnegligible lensinginduced bias for estimation of local nonGaussianity should be robustly treatable, and will only inflate f_{NL} error bars by a few percent over predictions where lensing effects are completely ignored (but note that lensing must still be accounted for to obtain unbiased constraints). We also show that the detection significance for the lensing bispectrum itself is ultimately limited to 9 sigma by cosmic variance. The tools that we develop for nonperturbative calculation of the lensing bispectrum are directly relevant to other calculations, and we give an explicit construction of a simple nonperturbative quadratic estimator for the lensing potential and relate its crosscorrelation power spectrum to the bispectrum. Our numerical codes are publicly available as part of CAMB and LensPix.
 Publication:

Journal of Cosmology and Astroparticle Physics
 Pub Date:
 March 2011
 DOI:
 10.1088/14757516/2011/03/018
 arXiv:
 arXiv:1101.2234
 Bibcode:
 2011JCAP...03..018L
 Keywords:

 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 32 pages, 10 figures