Power Spectrum Independent Constraints on Cosmological Models

Abstract

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$h^{-1}$Mpc 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.