POWER-SPECTRUM-INDEPENDENT CONSTRAINTS ON COSMOLOGICAL MODELS

A formalism is presented that allows cosmological experiments to be te sted for consistency and that allows a simple frequentist interpretati on of the resulting significance levels. As an example of an applicati on, this formalism is used to place constraints on bulk flows of galax ies using the results of the microwave background anisotropy experimen ts COBE and SP91, and a few simplifying approximations about the exper imental window functions. It is found that, if taken at face value, wi th the quoted errors, the recent detection by Lauer and Postman of a b ulk flow of 689 km s(-1) on scales of 150 h(-1) Mpc is inconsistent wi th SP91 at a 95% confidence level within the framework of a cold dark matter model. The same consistency test is also used to place constrai nts 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-di mensional optimization problem reduces to a set of coupled nonlinear e quations that can readily be solved numerically. Applying this techniq ue to the above-mentioned example, we find that the Lauer-Postman resu lt is inconsistent with SP91 even if no assumptions whatsoever are mad e about the power spectrum.