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The Aether Scalar Tensor (AeST) theory is an extension of General Relativity(GR), proposed for addressing galactic and cosmological observations withoutdark matter. By casting the AeST theory into a $3+1$ form, we determine itsfull non-perturbative Hamiltonian formulation and analyse the resultingconstraints. We find the presence of four first class and four second classconstraints and show that the theory propagates six degrees of freedom ongeneral backgrounds. We determine the case of small perturbations aroundMinkowski space as an example stemming from our analysis.

Aether scalar tensor theory: Hamiltonian Formalism