Max Tegmark's cosmology library: cl & Texas '96

You can get the 800K uncompressed postscript file by clicking here. The second paper described below is a brief conference proceeding which goes still further, making the power spectrum estimates uncorrelated, and is available here. Click here if you are interested in other research of mine.

Paper 1: How to measure CMB power spectra without losing information


Max Tegmark


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 n^2 rather than n^3, where n is the number of map pixels.
  4. It is applicable to any survey geometry whatsoever, with arbitraty regions masked out and arbitrary noise behaviour.
  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 futute high-resolution CMB experiments with n=10^6-10^7. It is also 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.

Reference info:

Phys. Rev. D, 55, 5895-5907 (1997)

Paper 2: Uncorrelated measurements of the CMB power spectrum


Max Tegmark & Andrew Hamilton


We describe how to compute estimates of the power spectrum C_l from Cosmic Microwave Background (CMB) maps that not only retain all the cosmological information, but also have uncorrelated error bars and well-behaved window functions. We apply this technique to the 4-year COBE/DMR data, and tabulate eight uncorrelated band-powers.

Reference info:

Preprint astro-ph/9702019.

Online references:

This site also contains the latest versions of some papers that are referenced in the text; Tegmark & Bunn 1995, Tegmark 1996a ("T96"), Tegmark , Taylor & Heavens 1996 ("TTH96"). Tegmark 1996b,

This figure summarizes the latest experimental results. Click on it for a postscript version, and click here for an online description of them with a data compilation and links.

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This page was last modified July 1, 1998.