The present and future of the most favoured inflationary models after
  $Planck$ 2015
  The value of the tensor-to-scalar ratio $r$ in the region allowed by the
latest $Planck$ 2015 measurements can be associated to a large variety of
inflationary models. We discuss here the potential of future Cosmic Microwave
Background cosmological observations in disentangling among the possible
theoretical scenarios allowed by our analyses of current $Planck$ temperature
and polarization data. Rather than focusing only on $r$, we focus as well on
the running of the primordial power spectrum, $\alpha_s$ and the running of
thereof, $\beta_s$. Our Fisher matrix method benefits from a detailed and
realistic appraisal of the expected foregrounds. Future cosmological probes, as
the COrE mission, may be able to reach an unprecedented accuracy in the
extraction of $\beta_s$ and rule out the most favoured inflationary models.
