We construct an inflation model with the inflaton non-minimally coupled to gravity on a warped Dvali–Gabadadze–Porrati brane. Using an exponential potential, we calculate the scalar power spectrum, spectral index and the running of the spectral index. We show that for a suitable range of non-minimal coupling it is possible to exit the inflationary phase spontaneously and without any mechanism, even in the case where minimal inflation cannot exit spontaneously. By means of a detailed analysis of parameter space, we study the constraints imposed on the non-minimal coupling from recent observational data.
