  Several extensions of General Relativity and high energy physics include
scalar fields as extra degrees of freedom. In the search for predictions in the
non-linear regime of cosmological evolution, the community makes use of
numerical simulations in which the quasi-static limit is assumed when solving
the equation of motion of the scalar field. In this Letter, we propose a method
to solve the full equations of motion for scalar degrees of freedom coupled to
matter. We run cosmological simulations which track the full time and space
evolution of the scalar field, and find striking differences with respect to
the commonly used quasi-static approximation. This novel procedure reveals new
physical properties of the scalar field and uncovers concealed astrophysical
phenomena which were hidden in the old approach.
