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However, this argument does not take into account the fact that mergers are not negligible at any scale in an Ω = 1 universe. In fact, stable clustering is more likely to be valid in models with Ω < 1 — a claim which seems to be again supported by simulations . ¯ x) cannot If stable clustering is valid, then the late time behaviour of ξ(a, be independent of initial conditions. In other words the two requirements: (i) validity of stable clustering at highly nonlinear scales and (ii) the independence of late time behaviour from initial conditions, are mutually exclusive.
A complete model of the universe taking into account all the fundamental interactions between the particles is therefore ruled out. A more feasible and productive approach is to treat large mass aggregates as the “particles” of the system and describe the universe in terms of the dynamics of these massive “particles” which are governed by gravity. This approach forms the basis of N 20 body simulations. An alternate approach involves averaging over the local velocities of the particles in a small volume and treating the volume itself as a fluid element and describe the system in terms of dynamics of a fluid.
The correspondence between structures in the full Nbody simulation is evident. verse and the equation of motion for the shell can be identified with the equation of growth of scale factor. 36) where A3 = GMB 2 (M is the total mass inside Ri ). 5 (n=-1. Power law spectrum). that the sphere will breakaway from the general expansion and reach a maximum radius at θ = π. 6. The final fate of the sphere will be an uninterrupted collapse towards a single point at θ = 2π. 7). To prevent the model from being driven towards a singularity one has to invoke a physical mechanism referred to as ‘virialisation’.