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We present a description for setting initial particle displacements and fieldvalues for simulations of arbitrary metric theories of gravity, for perfect andimperfect fluids with arbitrary characteristics. We extend the Zel'dovichApproximation to nontrivial theories of gravity, and show how scale dependenceimplies curved particle paths, even in the entirely linear regime ofperturbations. For a viable choice of Effective Field Theory of ModifiedGravity, initial conditions set at high redshifts are affected at the level ofup to 5% at Mpc scales, which exemplifies the importance of going beyond{\Lambda}-Cold Dark Matter initial conditions for modifications of gravityoutside of the quasi-static approximation. In addition, we show initialconditions for a simulation where a scalar modification of gravity is modelledin a Lagrangian particle-like description. Our description paves the way forsimulations and mock galaxy catalogs under theories of gravity beyond thestandard model, crucial for progress towards precision tests of gravity andcosmology.

Initial conditions for cosmological N-body simulations of the scalar sector of theories of Newtonian, Relativistic and Modified Gravity