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

Moslem Zarei

Published 2014-08-27, updated 2014-08-29Version 2

In conventional approaches, the power spectrum of primordial perturbations is characterized by free parameters such as the 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 summation over all of the running terms. In this method, we expand the power spectra about the pivot scale and then find the series terms as a function of e-folding number for models of inflation. Interestingly, for the models studied here one can sum over all terms and evaluate the exact form of power spectra. This in turn reduces the parameter space because in our method there are no spectral indexes and running terms. We compare our results to the recent CMB data and find that our new power spectra have good agreement with data although they contain less free parameters.