Compact (A)dS boson stars and shells

We present compact Q-balls in an (anti-)de Sitter background in D dimensions, obtained with a V-shaped potential of the scalar field. Beyond critical values of the cosmological constant Λ^_cr(D) compact Q-shells arise. By including the gravitational backreaction, we obtain boson stars and boson shells with (anti-)de Sitter asymptotics. We analyze the physical properties of these solutions and determine their domain of existence. In four dimensions we address some astrophysical aspects.