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We perform three-dimensional simulations of homogeneous and inhomogeneouscosmologies via the coupling of a numerical relativity code for spacetimeevolution and smoothed particle hydrodynamics (SPH) code. Evolution of a flatdust and radiation dominated Friedmann-Lema\^itre-Roberston-Walker (FLRW)spacetime shows an agreement of exact solutions with residuals on the order$10^{-6}$ and $10^{-3}$ respectively, even at low grid resolutions. Wedemonstrate evolution of linear perturbations of density, velocity and metricquantities to the FLRW with residuals of only $10^{-2}$ compared to exactsolutions. Finally, we demonstrate the evolution of non-linear perturbations ofthe metric past shell-crossing, such that dark matter halo formation ispossible. We show that numerical relativistic smoothed particle hydrodynamicsis a viable method for understanding non-linear effects in cosmology.

Inhomogeneous Cosmology using General Relativistic Smoothed Particle Hydrodynamics coupled to Numerical Relativity