Covariant Lagrange multiplier constrained higher derivative gravity with scalar projectors

Understand

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.