A control variate technique using differenced estimates from realistic masked and isotropic simulations reduces the computational cost of CMB lensing bias calculations by a factor of three to five.
CMB temperature lensing power reconstruction
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abstract
We study reconstruction of the lensing potential power spectrum from CMB temperature data, with an eye to the Planck experiment. We work with the optimal quadratic estimator of Okamoto and Hu, which we characterize thoroughly in application to reconstruction of the lensing power spectrum. We find that at multipoles L<250 our current understanding of this estimator is biased at the 15% level by beyond-gradient terms in the Taylor expansion of lensing effects. We present the full lensed trispectrum to fourth order in the lensing potential to explain this effect. We show that the low-L bias, as well as a previously known bias at high-L, is relevant to the determination of cosmology and must be corrected for in order to avoid significant parameter errors. We also investigate the covariance of the reconstructed power, finding broad correlations of ~0.1%. Finally, we discuss several small improvements which may be made to the optimal estimator to mitigate these problems.
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ACT DR6 yields a 2.3% precise CMB lensing power spectrum with A_lens = 1.013 ± 0.023 relative to Planck 2018 Lambda CDM, giving S8 = 0.818 ± 0.022 and no evidence for suppressed structure growth.
Estimators from squeezed bispectrum and collapsed trispectrum recover unbiased small-scale matter power spectrum covariance at the percent level using 25 Quijote simulations.
Planck PR4 maps with optimal filtering yield CMB lensing amplitude 1.004 ± 0.024 and σ8 Ωm^0.25 = 0.599 ± 0.016, the tightest lensing constraint yet.
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If at First You Don't Succeed, Trispectrum: I. Estimating the Matter Power Spectrum Covariance with Higher-Order Statistics
Estimators from squeezed bispectrum and collapsed trispectrum recover unbiased small-scale matter power spectrum covariance at the percent level using 25 Quijote simulations.