Newtonian N-body simulations are compatible with cosmological
  perturbation theory
  Contrary to recent claims in the literature, Newtonian N-body simulations of
collisionless Dark Matter in a LambdaCDM background are compatible with general
relativity and are not invalidated by general relativistic effects at the
linear level. This verdict is based on four facts. (1) The system of linearized
Einstein equations and conservation laws is well-posed in the gauge invariant
formulation and physically meaningful. (2) Comparing general relativity with
its Newtonian approximation at a given order in perturbation theory is only
meaningful at the level of observables. (3) The dynamics of observables
describing a dust fluid in general relativity and its Newtonian approximation
agree at the linear level. Any disagreement for observables on the lightcone
are well-known, of which the most dominant is gravitational lensing. (4) Large
fluctuations in the Hubble parameter contribute significantly only to
gravitational lensing effects. Therefore, these fluctuations are not in
conflict with Newtonian N-body simulations beyond what has already been
carefully taken into account using ray tracing technology.
