Planck 2018 results. X. Constraints on inflation
  We report on the implications for cosmic inflation of the 2018 Release of the
Planck CMB anisotropy measurements. The results are fully consistent with the
two previous Planck cosmological releases, but have smaller uncertainties
thanks to improvements in the characterization of polarization at low and high
multipoles. Planck temperature, polarization, and lensing data determine the
spectral index of scalar perturbations to be $n_\mathrm{s}=0.9649\pm 0.0042$ at
68% CL and show no evidence for a scale dependence of $n_\mathrm{s}.$ Spatial
flatness is confirmed at a precision of 0.4% at 95% CL with the combination
with BAO data. The Planck 95% CL upper limit on the tensor-to-scalar ratio,
$r_{0.002}<0.10$, is further tightened by combining with the BICEP2/Keck Array
BK15 data to obtain $r_{0.002}<0.056$. In the framework of single-field
inflationary models with Einstein gravity, these results imply that: (a)
slow-roll models with a concave potential, $V" (\phi) < 0,$ are increasingly
favoured by the data; and (b) two different methods for reconstructing the
inflaton potential find no evidence for dynamics beyond slow roll.
Non-parametric reconstructions of the primordial power spectrum consistently
confirm a pure power law. A complementary analysis also finds no evidence for
theoretically motivated parameterized features in the Planck power spectrum, a
result further strengthened for certain oscillatory models by a new combined
analysis that includes Planck bispectrum data. The new Planck polarization data
provide a stringent test of the adiabaticity of the initial conditions. The
polarization data also provide improved constraints on inflationary models that
predict a small statistically anisotropic quadrupolar modulation of the
primordial fluctuations. However, the polarization data do not confirm physical
models for a scale-dependent dipolar modulation.
