Contracting Cosmologies and the Swampland
  We consider the cosmology obtained using scalar fields with a negative
potential energy, such as employed to obtain an Ekpyrotic phase of contraction.
Applying the covariant entropy bound to the tower of states dictated by the
distance conjecture, we find that the relative slope of the potential
$|V^{\prime}| / |V|$ is bounded from below by a constant of the order one in
Planck units. This is consistent with the requirement to obtain slow Ekpyrotic
contraction. We also derive a refined condition on the potential which holds
near local minima of a negative potential.
