A Class of Minimally Modified Gravity Theories
  We investigate the Hamiltonian structure of a class of gravitational theories
whose actions are linear in the lapse function. We derive the necessary and
sufficient condition for a theory in this class to have two or less local
physical degrees of freedom. As an application we then find several concrete
examples of modified gravity theories in which the total number of local
physical degrees of freedom in the gravity sector is two.
