Constraints for the running index independent of the parameters of the model

By writing the running of the scalar spectral index completely in terms of the scalar index $n_s$ and the tensor-to-scalar ratio $r$ we are able to impose constraints to models of inflation which are independent of the parameters of the model in question. We write analytical expressions for the running index of Natural Inflation, two models of the type Mutated Hilltop Inflation and the Starobinsky model. The resulting formulae for the running depend exclusively on $n_s$ and/or $r$ and will keep tightening the running index further as additional conditions and observations constrain the scalar and the tensor-to-scalar indices.