# Reconstructing braneworld inflation

## TL;DR

This paper develops methods to reconstruct the effective potential of braneworld inflation models using parametrizations of the scalar spectral index and tensor-to-scalar ratio, providing specific examples under slow roll approximation.

## Contribution

It introduces a formalism for reconstructing braneworld inflation potentials from spectral index and tensor ratio parametrizations, with explicit examples for large N.

## Key findings

- Different effective potentials V(φ) are derived based on the chosen attractors.
- Constraints on model parameters are obtained for specific N-dependent attractors.
- Reconstruction methods are applicable within the slow roll approximation framework.

## Abstract

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.