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In this paper, we investigate the Randall-Sundrum type braneworld models inthe scalar-tensor theory with field derivative coupling to the Einstein tensor.We first formulate the generalized junction conditions of the metric and thescalar field on the timelike codimension-one hypersurface (=brane). With theuse of these junction conditions, we then derive the Minkowski and de Sitterbrane solutions embedded into the $Z_2$-symmetric five-dimensional anti-deSitter (AdS) bulk spacetime. The configuration of the scalar field depends onthe slice of the AdS spacetime. These branes are supported by the tension andnot coupled to the scalar field. The Minkowski brane solution can be obtainedwhen the brane tension is tuned to the bulk contributions. Once this tuningrelation is broken, the de Sitter brane solutions are obtained. The de Sitterbrane solutions have two branches. One has the smooth limit to the case wherethe scalar field becomes trivial, while the other branch does not. The latterbranch has the upper bound on the brane tension, where the expansion ratevanishes. Finally, we investigate the low energy effective gravitational theoryrealized on the brane, which is given by the four-dimensional Einstein-scalartheory with the corrections from the bulk. In the case that there is nogeneration of the dark radiation from the bulk scalar field, we recover the thefour-dimensional Einstein-scalar theory.

Braneworlds with field derivative coupling to the Einstein tensor