Large scale structure formation with the Schrödinger method
When describing large-scale structure formation of collisionless dark matter one is interested in the dynamics of a large collection of identical point particles that interact only gravitationally. Via gravitational instability initially small density perturbations evolve into eventually bound structures, like dark matter halos that are distributed along the cosmic web. Even though this problem seems quite simple from a conceptual point of view, no sufficiently general solution of the underlying equation, the collisionless Boltzmann equation coupled to the Poisson equation, is known. Therefore one usually has to resort to N-body simulations which tackle the problem numerically. Analytical methods to describe structure formation are in general based on the dust model which describes cold dark matter as a pressureless fluid characterized by density and velocity. This model works quite well up to the quasi-linear regime but eventually fails when multiple streams form that are especially important for halo formation but lead to singularities in the model. We employ the so-called Schrödinger method to develop a model which is able to describe multi-streaming and therefore can serve as theoretical N-body double and replacement for the dust model. As a first application we study the coarse-grained dust model, which is a limiting case of the Schrödinger method, within perturbation theory. On the basis of the Gaussian streaming model for redshift space distortions we predict the halo correlation function by generalizing the idea of the truncated Zeldovich approximation.