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The backreaction of inhomogeneities describes the effect of inhomogeneous structure on average properties of the Universe. We investigate this approach by testing the consistency of cosmological $N$-body simulations as non-linear structure evolves. Using the Delaunay Tessellation Field Estimator (DTFE), we calculate the kinematical backreaction $Q$ from simulations on different scales in order to measure how much $N$-body simulations should be corrected for this effect. This is the first step towards creating fully relativistic and inhomogeneous $N$-body simulations. In this paper we compare the interpolation techniques available in DTFE and illustrate the statistical dependence of $Q$ as a function of length scale.

Newtonian kinematical backreaction in cosmological N-body simulations with Delaunay Tesselation: “Zero test” and scale dependence