Max Tegmark's cosmology library: cl & Texas '96
You can get the 800K uncompressed
postscript file by clicking
The second paper described below is a brief conference proceeding
which goes still further, making the power spectrum estimates
uncorrelated, and is available here.
if you are interested in
other research of mine.
Paper 1: How to measure CMB power spectra without losing information
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:
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.
- It is unbeatable in the sense that no other method can measure
C_l with smaller error bars.
- It is quadratic, which makes the statistical properties of
the measurements easy to compute and use for estimation
of cosmological parameters.
- 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.
- It is applicable to any survey geometry whatsoever, with arbitraty
regions masked out and arbitrary noise behaviour.
- 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.
Phys. Rev. D, 55, 5895-5907 (1997)
Paper 2: Uncorrelated measurements of the CMB power spectrum
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.
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").
This figure summarizes the latest experimental results.
Click on it for a postscript version, and click
an online description of them with a data compilation and
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This page was last modified July 1, 1998.