Aether scalar-tensor theory: Hamiltonian formalism

The aether scalar-tensor (AeST) theory is an extension of general relativity, proposed for addressing galactic and cosmological observations without dark matter. By casting the AeST theory into a $3+1$ form, we determine its full nonperturbative Hamiltonian formulation and analyze the resulting constraints. We find the presence of four first class and four second class constraints and show that the theory has six physical degrees of freedom at the fully nonlinear level. Our results set the basis for determining the propagation of perturbations on general backgrounds and we present the case of small perturbations around Minkowski spacetime as an example stemming from our analysis.