Cornelius Rampf (Portsmouth University, United Kingdom)
Analytical methods have been fairly successful to understand the Newtonian regime of cosmological structure formation. Such methods are usually based on standard perturbation techniques which are however only approximative tools, and therefore might be not able to achieve the required accuracy to confront the theory with data from upcoming surveys. In this talk we show that it is actually possible to solve exactly for the non-linear fluid equations, if we consider an alternative approach to conventional perturbation theory. Indeed, in this talk it is shown that in a flat, cold dark matter (CDM) dominated Universe with positive cosmological constant (Λ), particle trajectories are analytical in time (representable by a convergent Taylor series) until at least a finite time after decoupling. The time variable used for this statement is the cosmic scale factor, i.e., the "a-time", and not the cosmic time. For this, a Lagrangian-coordinates formulation of the Euler-Poisson equations is employed. Temporal analyticity for ΛCDM is found to be a consequence of novel explicit all-order recursion relations for the a-time Taylor coefficients of the Lagrangian displacement field, from which we derive the convergence of the a-time Taylor series.