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