of the Randall–Sundrum braneworld theory without the scalar-curvature term in the action for the brane. In this paper, we are going to extend this analysis by investigating the case where this term is present in the action.

The scalar-curvature term for the brane was introduced in [@DGP] (see also [@CHS]) as a method of making gravity on the brane effectively four-dimensional even in the flat infinite bulk space. The corresponding cosmological models were initiated in [@CHS; @DDG]. The necessity of this term on the brane arises when one considers the complete effective action of the theory (see, e.g., [@HHR]). From this viewpoint, the term with brane tension represents the zero-order term in the expansion of the total action for the brane in powers of curvature of the induced metric, while the next term in the action for the brane is exactly the scalar-curvature Hilbert–Einstein term. From another (complementary) viewpoint [@DGP], this contribution is induced as a quantum correction to the effective action for the brane gravity after one takes into account the quantum character of the matter confined to the brane.

In this paper, we will show that the presence of the scalar-curvature term in the action for the brane 