  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.
