Consistency of the Hamiltonian formulation of the lowest-order effective action of the complete Horava theory

We perform the Hamiltonian analysis for the lowest-order effective action, up to second order in derivatives, of the complete Horava theory. The model includes the invariant terms that depend on partial derivative(i) lnN proposed by Blas, Pujolas, and Sibiryakov. We show that the algebra of constraints closes. The Hamiltonian constraint is of second-class behavior and it can be regarded as an elliptic partial differential equation for N. The linearized version of this equation is a Poisson equation for N that can be solved consistently. The preservation in time of the Hamiltonian constraint yields an equation that can be consistently solved for a Lagrange multiplier of the theory. The model has six propagating degrees of freedom in the phase space, corresponding to three even physical modes. When compared with the lambda R model studied by us in a previous paper, it lacks two second-class constraints, which leads to the extra even mode.