Simple inflationary models in Gauss-Bonnet brane-world cosmology

In light of the recent Planck 2015 results for the measurement of the CMB anisotropy, we study simple inflationary models in the context of the Gauss-Bonnet brane-world cosmology. The brane-world cosmological effect modifies the power spectra of scalar and tensor perturbations generated by inflation and causes a dramatic change for the inflationary predictions of the spectral index ($n_s$) and the tensor-to-scalar ratio ($r$) from those obtained in the standard cosmology. In particular, the power spectrum of tensor perturbation is suppressed due to the Gauss-Bonnet brane-world cosmological effect, which is in sharp contrast with inflationary scenario in the Randall-Sundrum brane-world cosmology where the power spectrum is enhanced. Hence, these two brane-world cosmological scenarios are distinguishable. With the dramatic change of the inflationary predictions, the inflationary scenario in the Gauss-Bonnet brane-world cosmology can be tested by more precise measurements of $n_s$ and future observations of the CMB $B$-mode polarization.