  We consider the prospects of probing features in the primordial power
spectrum with future Cosmic Microwave Background (CMB) polarization
measurements. In the scope of the inflationary scenario, such features in the
spectrum can be produced by local non-smooth pieces in an inflaton potential
(smooth and quasi-flat in general) which in turn may originate from fast phase
transitions during inflation in other quantum fields interacting with the
inflaton. They can fit some outliers in the CMB temperature power spectrum
which are unaddressed within the standard inflationary ${\mathrm{\Lambda}}$CDM
model. We consider Wiggly Whipped Inflation (WWI) as a theoretical framework
leading to improvements in the fit to the Planck 2015 temperature and
polarization data in comparison with the standard inflationary models, although
not at a statistically significant level. We show that some type of features in
the potential within the WWI models, leading to oscillations in the primordial
power spectrum that extend to intermediate and small scales can be constrained
with high confidence (at 3$\sigma$ or higher confidence level) by an instrument
as the Cosmic ORigins Explorer (CORE). In order to investigate the possible
confusion between inflationary features and footprints from the reionization
era, we consider an extended reionization history with monotonic increase of
free electrons with decrease in redshift. We discuss the present constraints on
this model of extended reionization and future predictions with CORE. We also
project, to what extent, this extended reionization can create confusion in
identifying inflationary features in the data.
