Gravitational stability of dark energy in galaxies and clusters of galaxies

Abstract

We analyze the behavior of the scalar field as dark energy of the Universe in a static world of galaxies and clusters of galaxies. We find the analytical solutions of evolution equations of the density and velocity perturbations of dark matter and dark energy, which interact only gravitationally, along with the perturbations of metric in a static world with background Minkowski metric. It was shown that quintessential and phantom dark energy in the static world of galaxies and clusters of galaxies is gravitationally stable and can only oscillate by the influence of self-gravity. In the gravitational field of dark matter perturbations, it is able to condense monotonically, but the amplitude of density and velocity perturbations on all scales remains small. It was also illustrated that the “accretion” of phantom dark energy in the region of dark matter overdensities causes formation of dark energy underdensities-the regions with negative amplitude of density perturbations of dark energy.