Aether scalar tensor theory: Hamiltonian Formalism

The Aether Scalar Tensor (AeST) theory is an extension of General Relativity (GR), proposed for addressing galactic and cosmological observations without dark matter. By casting the AeST theory into a $3+1$ form, we determine its full non-perturbative Hamiltonian formulation and analyse the resulting constraints. We find the presence of four first class and four second class constraints and show that the theory propagates six degrees of freedom on general backgrounds. We determine the case of small perturbations around Minkowski space as an example stemming from our analysis.