1204.1326 (Mark C. Neyrinck)

Quantifying distortions of the Lagrangian dark-matter mesh in cosmology    [PDF]

Mark C. Neyrinck

We examine the Lagrangian divergence of the displacement field, a more natural object than the density in a Lagrangian description of cosmological large-scale structure. This quantity, which we denote {\psi}, quantifies the stretching and distortion of the initially regular lattice of dark-matter particles in the universe. {\psi} encodes similar information as the density, but we find that even in the limit of vanishing fluctuations, a Gaussian distribution of {\psi} produces a density distribution much more lognormal than Gaussian. A local spherical-collapse-based (SC) fit found by Bernardeau gives a formula for {\psi}'s particle-by-particle behavior that works quite well, better than applying Lagrangian perturbation theory (LPT) at first or second (2LPT) order. In 2LPT, there is a roughly parabolic relation between initial and final {\psi} that can give overdensities in deep voids, so low-redshift, high-resolution 2LPT realizations should be used with caution. The SC fit excels at predicting {\psi} until streams cross; then, for particles forming haloes, {\psi} plummets as in a waterfall to -3. This gives a new method for producing particle realizations. Compared to LPT realizations, such SC realizations give reduced stream-crossing, and better visual and 1-point-PDF correspondence to the results of full gravity. LPT, on the other hand, predicts large-scale flows and the large-scale power-spectrum amplitude better, unless an empirical correction is added to the SC formula.

View original: http://arxiv.org/abs/1204.1326