The Structure of Structure Formation Theories

We study the general structure of models for structure formation, with applications to the reverse engineering of the model from observations. Through a careful accounting of the degrees of freedom in covariant gravitational instability theory, we show that the evolution of structure is completely speci ed by the stress history of the dark sector. The study of smooth, entropic, sonic, scalar anisotropic, vector anisotropic, and tensor anisotropic stresses reveals the origin, robustness, and uniqueness of speci c model phenomenology. We construct useful and illustrative analytic solutions that cover cases with multiple species of di ering equations of state relevant to the current generation of models, especially those with e ectively smooth components. We present a simple case study of models with phenomenologies similar to that of a CDM model to highlight reverse-engineering issues. A critical-density universe dominated by a single type of dark matter with the appropriate stress history can mimic a CDM model exactly.