Testing the Gravitational Instability Hypothesis?

We challenge a widely accepted assumption of observational cosmology: that successful reconstruction of observed galaxy density fields from measured galaxy velocity fields (or vice versa), using the methods of gravitational instability theory, implies that the observed large-scale structures and large-scale flows were produced by the action of gravity. This assumption is false, in that there exist non-gravitational theories that pass the reconstruction tests and gravitational theories with certain forms of biased galaxy formation that fail them. Gravitational instability theory predicts specific correlations between large-scale velocity and mass density fields, but the same correlations arise in any model where (a) structures in the galaxy distribution grow from homogeneous initial conditions in a way that satisfies the continuity equation, and (b) the present-day velocity field is irrotational and proportional to the time-averaged velocity field. We demonstrate these assertions using analytical arguments and N-body simulations of gravitational and non-gravitational models. We also show examples of gravitational and non-gravitational models that {\it fail} reconstruction tests because galaxy formation is modulated (``biased'') in a way that violates the continuity equation. We discuss the relation between the value of $\Omega$ inferred from velocity-density comparisons and the true cosmological value.