Primordial fluctuations and non-linear structure

Abstract

We explore several aspects of non-linear gravitational instability using two numerical experiments, each of which employs a series of 3D cosmological N-body simulations. In the first experiment we truncate all of the initial high-frequency power above some critical wavenumber kc; in the second experiment, we replace initial Fourier components with wavenumbers |$k\gt{k}_\text{c}$| by waves taken from an independent realization with the same power spectrum but with unrelated phases. We evolve these initial conditions for different values of kc to see how the progressive elimination or substitution of initial high-frequency components affects the final, non-linear structure. We find that such structure is determined mainly by initial waves with |$k\lesssim{k}_{1}\sim R_{1}^{-1},\,\text{where}\,{R}_{1}$| is the comoving scale on which rms fluctuations are just becoming non-linear. Changes in high-frequency components of the initial conditions do not disturb the evolution of longer waves, and even on small scales the influence of waves with |$k\gt{k}_{1}$| is erased by gravitational collapse. Since fluctuations with |${k}\ll {k}_{1}$| are weak, we conclude that the appearance of non-linear structure in the universe is determined by fluctuations from a fairly small range in wavenumber. Our first experiment also confirms that a truncated initial power spectrum leads to coherent, large-scale filamentary structures when |${k}_\text{c}\sim {k}_{1}.$|