By the application of the generalized Israel junction conditions we derive cosmological equations for the fourth-order $f(R)$ brane gravity and study their cosmological solutions. We show that there exists a nonstatic solution which describes a four-dimensional de Sitter $({\mathrm{dS}}_4)$ brane embedded in a five-dimensional anti-de Sitter $({\mathrm{AdS}}_5)$ bulk for a vanishing Weyl tensor contribution. On the other hand, for the case of a nonvanishing Weyl tensor contribution, there exists a static brane solution only. We claim that in order to get some more general nonstatic $f(R)$ brane configurations, one needs to admit a dynamical matter energy-momentum tensor in the bulk rather than just a bulk cosmological constant.

• Received 14 April 2010

DOI:https://doi.org/10.1103/PhysRevD.81.123527