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 $\delta_A(x, t_{initial})=-\delta_B(x,t_{initial})$ (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 {\Lambda}CDM initial conditions, and in the linear regime evolve identically up to the overall sign. As non-linear 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.