Exploring Cosmic Origins with CORE: Inflation
  We forecast the scientific capabilities to improve our understanding of
cosmic inflation of CORE, a proposed CMB space satellite submitted in response
to the ESA fifth call for a medium-size mission opportunity. The CORE satellite
will map the CMB anisotropies in temperature and polarization in 19 frequency
channels spanning the range 60-600 GHz. CORE will have an aggregate noise
sensitivity of $1.7 \mu$K$\cdot \,$arcmin and an angular resolution of 5' at
200 GHz. We explore the impact of telescope size and noise sensitivity on the
inflation science return by making forecasts for several instrumental
configurations. This study assumes that the lower and higher frequency channels
suffice to remove foreground contaminations and complements other related
studies of component separation and systematic effects, which will be reported
in other papers of the series "Exploring Cosmic Origins with CORE." We forecast
the capability to determine key inflationary parameters, to lower the detection
limit for the tensor-to-scalar ratio down to the $10^{-3}$ level, to chart the
landscape of single field slow-roll inflationary models, to constrain the epoch
of reheating, thus connecting inflation to the standard radiation-matter
dominated Big Bang era, to reconstruct the primordial power spectrum, to
constrain the contribution from isocurvature perturbations to the $10^{-3}$
level, to improve constraints on the cosmic string tension to a level below the
presumptive GUT scale, and to improve the current measurements of primordial
non-Gaussianities down to the $f_{NL}^{\rm local} < 1$ level. For all the
models explored, CORE alone will improve significantly on the present
constraints on the physics of inflation. Its capabilities will be further
enhanced by combining with complementary future cosmological observations.
