Abstract

Based on perturbation theory, we study the dynamics of how dark matter and dark energy in the collapsing system approach dynamical equilibriumwhen they are in interaction. We find that the interaction between dark sectors cannot ensure the dark energy to fully cluster along with darkmatter. When dark energy does not trace dark matter, we present a new treatment on studying the structure formation in the spherical collapsingsystem. Furthermore we examine the cluster number counts dependence on the interaction between dark sectors and analyze how dark energyinhomogeneities affect cluster abundances. It is shown that cluster number counts can provide specific signature of dark sectors interaction anddark energy inhomogeneities.

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