According to the standard model of elementary particles, the intermediate bosons of the weak interaction were massless before the Higgs transition at approximately 10-11s after the Big Bang1, making this interaction long-ranged. We present here a new hamiltonian formulation of the Einstein-Yang-Mills (EYM) system that classically couples gravity and the weak force. These equations have been widely studied in the last decade but very few results are known for inhomogeneous dynamical gravitational fields. Our purpose is thus to use this formulation to study, e.g. the evolution of density fluctuations before the Higgs transition that could lead to those of the Cosmic Microwave Background. Here, we focus on Yang-Mills fields only, but in a near future we intend to add scalar (Higgs) and spinor (leptons) fields to our model.
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