  The group of compactly supported Hamiltonian diffeomorphisms of a symplectic
manifold is endowed with a natural bi-invariant distance, due to Viterbo,
Schwarz, Oh, Frauenfelder and Schlenk, coming from spectral invariants in
Hamiltonian Floer homology. This distance has found numerous applications in
symplectic topology. However, its diameter is still unknown in general. In
fact, for closed symplectic manifolds there is no unifying criterion for the
diameter to be infinite. In this paper, we prove that for any Liouville domain
this diameter is infinite if and only if its symplectic cohomology does not
vanish. This generalizes a result of Monzner-Vichery-Zapolsky and has
applications in the setting of closed symplectic manifolds.
