When dealing with structure formation in Cosmology, it's often said that well inside the Hubble radius we can use Newtonian gravity and therefore the starting point to obtain equations for the perturbations in matter density is the well known Poisson equation.
However, I don't see the relation between both things: Hubble radius and whether I can use Newton's laws or not. Actually, inside the Hubble radius galaxies are interacting among themselves so in principle that should be ruled by General Gravity unless the fields are really weak. Is that the reason why? Are galaxies so far away from each other that the gravitational fields are truly weak, hence we can make use of Newtonian gravity?
But in that case, it would be the distance among galaxies and not the Hubble radius the reason for flat spacetime.