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On the joint analysis of CMB temperature and lensing-reconstruction power spectra
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Gravitational lensing provides a significant source of cosmological information in modern CMB parameter analyses. It is measured in both the power spectrum and trispectrum of the temperature fluctuations. These observables are often treated as independent, although as they are both determined from the same map this is impossible. In this paper, we perform a rigorous analysis of the covariance between lensing power spectrum and trispectrum analyses. We find two dominant contributions coming from: (i) correlations between the disconnected noise bias in the trispectrum measurement and sample variance in the temperature power spectrum; and (ii) sample variance of the lenses themselves. The former is naturally removed when the dominant N0 Gaussian bias in the reconstructed deflection spectrum is dealt with via a partially data-dependent correction, as advocated elsewhere for other reasons. The remaining lens-cosmic-variance contribution is easily modeled but can safely be ignored for a Planck-like experiment, justifying treating the two observable spectra as independent. We also test simple likelihood approximations for the deflection power spectrum, finding that a Gaussian with a parameter-independent covariance performs well.
Forward citations
Cited by 5 Pith papers
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The Atacama Cosmology Telescope: A Measurement of the DR6 CMB Lensing Power Spectrum and its Implications for Structure Growth
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.
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Optimal filtering for CMB lensing reconstruction
Optimal anisotropic CMB filtering plus a second-stage filter on the reconstructed lensing convergence map reduces lensing power spectrum variance by factor 2-5 relative to isotropic filtering, with up to 30% additiona...
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