Lost in k-space?


Fig 1: Latest constraints on the linear matter power spectrum
Here's a combination of all data as of July 2002 taking into account calibration and beam errors (click on it for ps):
Here are text files with the corresponding data, window functions and correlation matrix. The window function file above contains 25 columns, giving the window functions W_l for each of the 25 band power measurements with the convention
(dT)^2 = sum W_l (dT_l)^2 = sum l(l+1) W_l C_l/2 pi.
Note that this differs from the traditional definition by a factor of l - it's more approptiate to think of the band power as an average on a linear plot rather than on a log-plot now that we're all plotting small-scale CMB data with a linear l-axis. Also, note that some of these window functions go slightly negative, and that that's OK. Note that the file gives not the covariance matrix but the dimensionless correlation matrix R, which is related to the covariance matrix C by
C_ij = R_ij sigma_i sigma_j.
To test a model against this data, put the first 2000 values of dT_l^2 = l(l+1) C_l/2 pi into a vector c and compute
chi2 = (q-Wc)^t C^{-1} (q-Wc),
where q is our vector of 25 data points and W is our window matrix. You'll find more data details and links here.

Separating the Early Universe from the Late Universe:
cosmological parameter estimation beyond the black box

Please click here to download our paper.
Click here if you are interested in other research of mine. 

Authors:

Max Tegmark, Matias Zaldarriaga

Abstract:

We present a method for measuring the cosmic matter budget without assumptions about speculative Early Universe physics, and for measuring the primordial power spectrum P*(k) non-parametrically, either by combining CMB and LSS information or by using CMB polarization. Our method complements currently fashionable ``black box'' cosmological parameter analysis, constraining cosmological models in a more physically intuitive fashion by mapping measurements of CMB, weak lensing and cluster abundance into k-space, where they can be directly compared with each other and with galaxy and Lyman alpha forest clustering. Including the new CBI results, we find that CMB measurements of P(k) overlap with those from 2dF galaxy clustering by over an order of magnitude in scale, and even overlap with weak lensing measurements. We describe how our approach can be used to raise the ambition level beyond cosmological parameter fitting as data improves, testing rather than assuming the underlying physics.

Reference info:

astro-ph/0207047, Phys. Rev. D, in press
Return to my home page
This page was last modified October 6, 2002.
max@physics.upenn.edu