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# Revisiting Vainshtein Screening for fast N-body simulations

Mar 2023

We revisit a method to incorporate the Vainshtein screening mechanism inN-body simulations proposed by R. Scoccimarro in~\cite{Scoccimarro:2009eu}. Wefurther extend this method to cover a subset of Horndeski theories that evadethe bound on the speed of gravitational waves set by the binary neutron starmerger GW170817. The procedure consists of the computation of an effectivegravitational coupling that is time and scale dependent, $G_{\rmeff}\left(k,z\right)$, where the scale dependence will incorporate thescreening of the fifth-force. This is a fast procedure that when contrasted tothe alternative of solving the full equation of motion for the scalar fieldinside N-body codes, reduces considerably the computational time and complexityrequired to run simulations. To test the validity of this approach in thenon-linear regime, we have implemented it in a COmoving LagrangianApproximation (COLA) N-body code, and ran simulations for two gravity modelsthat have full N-body simulation outputs available in the literature, nDGP andCubic Galileon. We validate the combination of the COLA method with thisimplementation of the Vainshtein mechanism with full N-body simulations forpredicting the boost function: the ratio between the modified gravitynon-linear matter power spectrum and its General Relativity counterpart. Thisquantity is of great importance for building emulators in beyond-$\Lambda$CDMmodels, and we find that the method described in this work has an agreement ofbelow $2\%$ for scales down to $k \approx 3h/$Mpc with respect to full N-bodysimulations.

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