Covariant Lagrange multiplier constrained higher derivative gravity with
  scalar projectors
  We formulate higher derivative gravity with Lagrange multiplier constraint
and scalar projectors. Its gauge-fixed formulation as well as vector fields
formulation is developed and corresponding spontaneous Lorentz symmetry
breaking is investigated. We show that the only propagating mode is higher
derivative graviton while scalar and vector modes do not propagate. Despite to
higher derivatives structure of the action, its first FRW equation is the first
order differential equation which admits the inflationary universe solution.
