Viable curvaton models from the fNL parameter

In this paper, we propose a method to reconstruct the curvaton potential from a scale-dependent non-Gaussianity parameter fNL. We exemplify our method, devising a weakly self-interacting curvaton model that produces a scale-dependent fNL that crosses zero twice and is bounded from below and above. We identify the higher value of crossing with the cosmic microwave background (CMB) pivot scale, making the lower value fall within important structure formation scales. In addition, our curvaton model satisfies the observational constraints and leads to a k -dependent fNL that can explain the CMB dipolar modulation. Our procedure can be straightforwardly extended to reconstruct the curvaton potential instead from the gNL parameter.