  The application of numerical relativity to cosmological spacetimes is
providing new insights into the behavior of Einstein's equations, beyond common
approximations. In order for simulations to be performed as accurately and
efficiently as possible, we investigate a novel formulation of Einstein's
equations. This formulation evolves differences from a "reference" solution
describing the dominant behavior of the spacetime, which mitigates error due to
both truncation and approximate finite difference calculations. We find that
the error in solutions obtained using the reference formulation can be smaller
by an order of magnitude or more, with the level of improvement depending on
how well the reference solution approximates the exact solution.
