  Cosmological simulations involving the fully covariant gravitational dynamics
may prove relevant in understanding relativistic/non-linear features and,
therefore, in taking better advantage of the upcoming large scale structure
survey data. We propose a new 3+1 integration scheme for General Relativity in
the case where the matter sector contains a minimally-coupled perfect fluid
field. The original feature is that we completely eliminate the fluid
components through the constraint equations, thus remaining with a set of
unconstrained evolution equations for the rest of the fields. This procedure
does not constrain the lapse function and shift vector, so it holds in
arbitrary gauge and also works for arbitrary equation of state. An important
advantage of this scheme is that it allows one to define and pass an adaptation
of the robustness test to the cosmological context, at least in the case of
pressureless perfect fluid matter, which is the relevant one for late-time
cosmology.
