How to measure CMB power spectra without losing information

1996/11/30 by Max Tegmark · 13 citations
Physics and Astronomy · #Cosmology and Gravitation Theories #Galaxies: Formation, Evolution, Phenomena #Scientific Research and Discoveries #astro-ph

paper · pdf · doi:10.1103/physrevd.55.5895

published as Phys.Rev.D55:5895-5907,1997 · 22 pages, with 8 figures included. Minor revisions to match accepted version. Color figures and data at http://www.sns.ias.edu/~max/cl.html (faster from the US), from http://www.mpa-garching.mpg.de/~max/cl.html (faster from Europe) or from [email protected]

arxiv created 1997/03/12 · openalex publication_date 1997/05/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new method for estimating the angular power spectrum C_l from cosmic microwave background (CMB) maps is presented, which has the following desirable properties. (1) It is unbeatable in the sense that no other method can measure C_l with smaller error bars. (2) It is quadratic, which makes the statistical properties of the measurements easy to compute and use for estimation of cosmological parameters. (3) It is computationally faster than rival high-precision methods such as the nonlinear maximum-likelihood technique, with the crucial steps scaling as n² rather than n³, where n is the number of map pixels. (4) It is applicable to any survey geometry whatsoever, with arbitrary regions masked out and arbitrary noise behavior. (5) It is not a ``black-box'' method, but quite simple to understand intuitively: it corresponds to a high-pass filtering and edge softening of the original map followed by a straight expansion in truncated spherical harmonics. It is argued that this method is computationally feasible even for future high-resolution CMB experiments with n\ensuremath∼10⁶--10⁷. It is shown that C_l computed with this method is useful not merely for graphical presentation purposes, but also as an intermediate (and arguably necessary) step in the data analysis pipeline, reducing the data set to a more manageable size before the final step of constraining Gaussian cosmological models and parameters --- while retaining all the cosmological information that was present in the original map.

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• Non-detection of a statistically anisotropic power spectrum in large-scale structure
• Optimized supernova constraints on dark energy evolution
• Is the Universe infinite or is it just really big?
• A Measurement of the Angular Power Spectrum of the Cosmic Microwave Background from [CLC][ITAL]l[/ITAL][/CLC] = 100 to 400
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• The power spectrum from the angular distribution of galaxies in the CFHTLS-Wide fields at redshift ∼0.7
• TEASING: a fast and accurate approximation for the low multipole likelihood of the cosmic microwave background temperature