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 Zeldovich Approximation to no
ntrivial 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.
We argue that there is an intrinsic noise on measurements of the equation of state parameter $w=p/rho$ from large-scale structure around us. The presence of the large-scale structure leads to an ambiguity in the definition of the background universe
and thus there is a maximal precision with which we can determine the equation of state of dark energy. To study the uncertainty due to local structure, we model density perturbations stemming from a standard inflationary power spectrum by means of the exact Lema^{i}tre-Tolman-Bondi solution of Einsteins equation, and show that the usual distribution of matter inhomogeneities in a $Lambda$CDM cosmology causes a variation of $w$ -- as inferred from distance measures -- of several percent. As we observe only one universe, or equivalently because of the cosmic variance, this uncertainty is systematic in nature.
