Reconstructing braneworld inflation

The reconstruction of a braneworld inflationary universe considering the parametrization (or attractor) of the scalar spectral index $n_s(N)$ in terms of the number of $e$-foldings 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 $n_s(N)$ 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 $n_s-1\propto N^{-1}$ for the scalar spectral index and the attractor $r\propto N^{-2}$ for the tensor to scalar ratio. In this context and depending on the attractors used, we find different expressions for the effective potential $V(\phi)$, as also the constraints on the parameters present in the reconstruction.