Inverted initial conditions: Exploring the growth of cosmic structure and voids

We introduce and explore "paired" cosmological simulations. A pair consists of an A and B simulation with initial conditions related by the inversion δ_A(x ,t_initial)=-δ_B(x ,t_initial) (underdensities substituted for overdensities and vice versa). We argue that the technique is valuable for improving our understanding of cosmic structure formation. The A and B fields are by definition equally likely draws from Λ CDM initial conditions, and in the linear regime evolve identically up to the overall sign. As nonlinear evolution takes hold, a region that collapses to form a halo in simulation A will tend to expand to create a void in simulation B. Applications include (i) contrasting the growth of A-halos and B-voids to test excursion-set theories of structure formation, (ii) cross-correlating the density field of the A and B universes as a novel test for perturbation theory, and (iii) canceling error terms by averaging power spectra between the two boxes. Generalizations of the method to more elaborate field transformations are suggested.