On the running of the spectral index to all orders: a new model dependent approach to constrain inflationary models

TL;DR

This paper introduces a new model-dependent approach to exactly compute primordial power spectra for simple inflationary models by resumming all running terms, leading to more precise predictions consistent with CMB data.

Contribution

It presents a novel method to sum all spectral running terms for inflationary potentials, providing exact power spectra and improved model parametrizations.

Findings

Exact power spectra can be derived for certain inflationary models.

The new spectra show good agreement with recent CMB observations.

Resumming all running terms enhances the accuracy of inflationary predictions.

Abstract

In conventional model independent approaches, the power spectrum of primordial perturbations is characterized by such free parameters as spectral index, its running, the running of running, and the tensor-to-scalar ratio. In this work we, show that, at least for simple inflationary potentials, one can find the primordial scalar and tensor power spectra exactly by resumming over all the running terms. In this model-dependent method, we expand the power spectra about the pivot scale to find the series terms as functions of the e-folding number for some single field models of inflation. Interestingly, for the viable models studied here, one can sum over all the terms and evaluate the exact form of the power spectra. This in turn gives more accurate parametrization of the specific models studied in this work. We finally compare our results with the recent cosmic microwave background data to find that our new power spectra are in good agreement with the data.