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

Understand

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.