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

TL;DR

This paper derives model-independent constraints on the running of the scalar spectral index in inflationary models by expressing it solely in terms of observable parameters like $n_s$ and $r$, enabling tighter bounds as data improves.

Contribution

It provides analytical formulas for the running index that depend only on observable parameters, applicable to various inflation models, independent of their specific parameters.

Findings

Derived expressions for the running index in Natural Inflation, Mutated Hilltop Inflation, and Starobinsky models.

Formulas depend only on $n_s$ and $r$, facilitating model-independent constraints.

Framework allows tightening of bounds with future observational data.

Abstract

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.