Max Tegmark's library: pindep.ps
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POWER SPECTRUM INDEPENDENT CONSTRAINTS ON COSMOLOGICAL MODELS
Authors: Max Tegmark, Ted Bunn & Wayne Hu
A formalism is presented that allows cosmological
experiments to be tested for consistency, and allows a simple
frequentist interpretation of the resulting significance levels.
As an example of an application, this formalism is used to place
constraints on bulk flows of galaxies using the results of the microwave
background anisotropy experiments COBE and SP91, and a few simplifying
approximations about the experimental window functions.
It is found that if taken at face value, with the quoted errors,
the recent detection by Lauer and Postman of a bulk flow of 689 km/s
on scales of 150 Mpc/h is inconsistent with SP91 at a 95%
confidence level within the framework of a Cold Dark Matter (CDM) model.
The same consistency test is also used to place constraints that are
completely model-independent, in the sense that they hold for any
power spectrum whatsoever - the only assumption being that the random
fields are Gaussian. It is shown that the resulting infinite-dimensional
optimization problem reduces to a set of coupled non-linear equations
that can readily be solved numerically.
Applying this technique to the above-mentioned example, we find that the
Lauer and Postman result is inconsistent with SP91 even if no
assumptions whatsoever are made about the power spectrum.
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This page was last modified July 1, 1998.