Morphology in Cosmological Gravitational Clustering and Catastrophe Theory

概要

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Non-linear growth of cosmological density fluctuations from initial small flucuations with a non-scale-free power spectrum is analyzed in three-dimensional systems. It is found that after the first appearance of singularities (caustics) of density the power spectrum of the density fields obeys a power law even on small scales below the cutoff scale of the initial power spectrum. The value of the power index on these scales is approximately -3, irrespective of the power index n of the initial power spectrum above the cutoff scale of the initial power spectrum when the cutoff scale is large. In this case, sheet structures of the particle distribution (the ''sheet'' shape of caustics of article trajectories) clearly appear at random places. It is shown that the power index on small scales below the typical size of the thickness of sheets is determined only by the type of the singularities (caustics), irrespective of the detailed initial conditions. The type of the singularity is classified in accord with the catastrophe theory. In the above case, the A2 type (sheet structure) of singularities dominates other types of singularities after the first appearance of caustics, and this is the reason the value of the power index is close to -3. This argument can be applied also in one-dimensional and two-dimensional systems.
理論物理学刊行会の論文
1998-01-25