Swampland Distance Conjecture, Inflation and $\alpha$-attractors
  The Swampland Distance Conjecture (SDC) constraints the dynamics emerging at
infinite distances in field space of any effective field theory consistent with
quantum gravity. It provides a relation between the cut-off in energies and the
field range which, as we show, in the context of inflation it yields a
universal upper bound on the inflaton excursion in terms of the
tensor-to-scalar ratio, measured at typical CMB scales. In this note, we
investigate the interplay between the SDC and the emergent inflationary physics
around infinite distances singularities in string theory, with a special look
at its significance for the $\alpha$-attractor scenario of inflation. We show
that the conjecture itself suggests that inflation may arise as an infinite
distance phenomenon with the asymptotic kinetic structure typical of
$\alpha$-attractors. Furthermore, we argue that a proper string realisation of
these cosmological models in Calabi-Yau manifolds should occur around infinite
field distance singularities. However, such constructions typically imply that
inflation should not take place in the limit where the inflaton kinetic term
develops a pole but rather in the opposite regime. Finally, we study the
constraints that the SDC poses on $\alpha$-attractors and show that they still
leave considerable room for compatibility with observations.
