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The brane-world scenario provides an intriguing possibility to explore thephenomenological cosmology implied by string/M theory. In this paper, weconsider a modified Randall-Sundrum single brane model with two naturalgeneralizations: a Gauss-Bonnet term in the five-dimensional bulk action aswell as an induced gravity term in the four-dimensional brane action, which arethe leading-order corrections to the Randall-Sundrum model. We study theinfluence of these combined effects on the evolution of the primordialgravitational waves generated during an extreme slow-roll inflation on thebrane. The background, for the early inflationary era, is then modeled througha de Sitter brane embedded within an anti-de Sitter bulk. In this framework, weshow that both effects tend to suppress the Randall-Sundrum enhancement of theamplitude of the tensor perturbations at relatively high energies. Moreover,the Gauss-Bonnet effect, relative to standard general relativity, will abruptlyenhance the tensor-to-scalar ratio and break the standard consistency relationat high energies, which cannot be evaded by invoking the induced gravityeffect, even though the induced gravity strength would mildly counterbalancethese significant changes at high energies. We note that the brane-world modelwith or without the induced gravity effect fulfills the consistency relation.Finally, we discuss some implications of the observational constraints.

Tensor Perturbations from Brane-World Inflation with Curvature Effects