Inflation, Higher Spins and the Swampland
  We study the implications on inflation of an infinite tower of higher-spin
states with masses falling exponentially at large field distances, as dictated
by the Swampland Distance Conjecture. We show that the Higuchi lower bound on
the mass of the tower automatically translates into an upper bound on the
inflaton excursion. Strikingly, the mere existence of all spins in the tower
forbids any scalar displacement whatsoever, at arbitrarily small Hubble scales,
and it turns out therefore incompatible with inflation. A certain field
excursion is allowed only if the tower has a cut-off in spin. Finally, we show
that this issue is circumvented in the case of a tower of string excitations
precisely because of the existence of such a cut-off, which decreases fast
enough in field space.
