  A contact manifold admittting a supporting contact form without contractible
Reeb orbits is called hypertight. In this paper we construct a Rabinowitz Floer
homology associated to an arbitrary supporting contact form for a hypertight
contact manifold, and use this to prove versions of conjectures of Sandon and
Mazzucchelli on the existence of translated points and invariant Reeb orbits,
and to show that positive loops of contactomorphisms give rise to
non-contractible Reeb orbits.
