The Einstein-scalar field constraints on asymptotically Euclidean   manifolds
  We use the conformal method to obtain solutions of the Einstein-scalar field gravitational constraint equations. Handling scalar fields is a bit more challenging than handling matter fields such as fluids, Maxwell fields or Yang-Mills fields, because the scalar field introduces three extra terms into the Lichnerowicz equation, rather than just one. Our proofs are constructive and allow for arbitrary dimension (>2) as well as low regularity initial data. 
Yvonne Choquet-Bruhat, James Isenberg and Daniel Pollack