Reconstructing braneworld inflation

The reconstruction of a braneworld inflationary universe considering the parametrization (or attractor) of the scalar spectral index ns(N) in terms of the number of e-folding N is developed. We also study the possibility that the reconstruction for the scenario of braneworld inflation can be realized in terms of the tensor-to-scalar ratio r(N). For both reconstruction methodologies, we consider a general formalism in order to obtain the effective potential as a function of the cosmological parameters ns(N) or r(N). For both reconstruction methods, we consider the specific examples for large N in the framework of the slow-roll approximation as the attractor ns-1N-1 for the scalar spectral index and the attractor rN-2 for the tensor-to-scalar ratio. In this context and depending on the attractors used, we find different expressions for the effective potential V(φ), as also the constraints on the parameters present in the reconstruction.