Comparison of the velocity distribution between the adhesion approximation and the Euler-Jeans-Newton model

Abstract

For the evolution of density fluctuation in nonlinear cosmological dynamics, adhesion approximation (AA) is proposed as a phenomenological model, which is especially useful for describing nonlinear evolution. However, the origin of the artificial viscosity in AA is not clarified. Recently, Buchert and Dom\'{\i}nguez report if the velocity dispersion of the dust fluid is regarded as isotropic, it works on a principle similar to viscosity or effective pressure, and they consider isotropic velocity dispersion as the origin of the artificial viscosity in AA. They name their model the Euler-Jeans-Newton (EJN) model. In this paper, we focus on the velocity distribution in AA and the EJN model and examine the time evolution in both models. We find the behavior of AA differs from that of the EJN model, i.e., although the peculiar velocity in the EJN model oscillates, that in AA is monotonically decelerated due to viscosity without oscillation. Therefore it is hard to regard viscosity in AA as effective pressure in the EJN model.