Speaker: Cornelius Rampf
I present an introduction of Lagrangian fluid-flow approaches to the cosmological structure formation, in both the Newtonian theory and in General Relativity. In the first part of the talk I report some important achievements and current efforts related to the Newtonian Lagrangian perturbation theory. I show that it is actually possible to obtain exact perturbative solutions for the fully non-linear fluid equations in Lagrangian space. In the second part of the talk I show how the Lagrangian fluid-flow approach can be generalised to General Relativity. The necessity of such a generalisation is, that current and forthcoming surveys will resolve the large-scale structure of the Universe with unprecedented accuracy, and will reduce uncertainties in the cosmological model to the per cent level. However, general relativistic corrections to the dominating Newtonian part are generally expected to be of similar magnitude. Thus, it is important to constrain general relativistic effects to sufficient accuracy, preferably in a framework which comes with simple physical interpretations. For this purpose, a relativistic Lagrangian-Eulerian description is a very powerful tool since it also contains transferable output which can be e.g. used to set up relativistic initial conditions for numerical N-body simulations, or to apply relativistic biasing schemes.