Observational constraints on a hyperbolic potential in brane-world inflation

We focus on the large field of a hyperbolic potential form, which is characterized by a parameter f , in the framework of the brane-world inflation in Randall-Sundrum-II model. From the observed form of the power spectrum P R ( k ), the parameter f should be of order 0.1 m p to 0.001 m p , the brane tension must be in the range λ ~ (1−10)×10 57 GeV 4 , and the energy scale is around V 0 1/4 ~ 10 15 GeV. We find that the inflationary parameters ( n s , r , and dn s / d (ln k ) depend only on the number of e-folds N . The compatibility of these parameters with the last Planck measurements is realized with large values of N .