Generalized Randall-Sundrum model with a single thick brane

A generalized version of the Randall-Sundrum model-2 with different cosmological constants on each side of a brane is discussed. The possibility of replacing the singular brane by a configuration of a scalar field is also considered, the Einstein equations for this setup are solved, and the stability of the solution is discussed. It is shown that under mild assumptions the relation between the cosmological constants and the brane tension obtained in the brane limit does not depend on the particular choice of the regularizing profile of the scalar field.