Initial conditions for cosmological N-body simulations of the scalar
  sector of theories of Newtonian, Relativistic and Modified Gravity
  We present a description for setting initial particle displacements and field
values for simulations of arbitrary metric theories of gravity, for perfect and
imperfect fluids with arbitrary characteristics. We extend the Zel'dovich
Approximation to nontrivial theories of gravity, and show how scale dependence
implies curved particle paths, even in the entirely linear regime of
perturbations. For a viable choice of Effective Field Theory of Modified
Gravity, initial conditions set at high redshifts are affected at the level of
up to 5% at Mpc scales, which exemplifies the importance of going beyond
{\Lambda}-Cold Dark Matter initial conditions for modifications of gravity
outside of the quasi-static approximation. In addition, we show initial
conditions for a simulation where a scalar modification of gravity is modelled
in a Lagrangian particle-like description. Our description paves the way for
simulations and mock galaxy catalogs under theories of gravity beyond the
standard model, crucial for progress towards precision tests of gravity and
cosmology.
