How well is our Universe described by an FLRW model?

Extremely well! The spacetime metric, gab, of our universe is approximated by an FLRW metric, g (0) ab, to about 1 part in 10 4 or better on both large and small scales, except in the immediate vicinity of very strong field objects, such as black holes. However, derivatives of gab are not close to derivatives of g (0) ab, so there can be significant differences in the behavior of geodesics and huge differences in curvature. Consequently, observable quantities in the actual universe may differ significantly from the corresponding observables in the FLRW model. Nevertheless, as we shall review here, we have proven general results showing that the large matter inhomogeneities that occur on small scales cannot produce significant backreaction effects on large scales, so g (0) ab satisfies Einstein’s equation with the averaged stress-energy tensor of matter as its source. We discuss the flaws in some other approaches that have suggested that large backreaction effects may occur. As we also will review here, with a suitable “dictionary, ” Newtonian cosmologies provide excellent approximations to cosmological solutions to Einstein’s equation (with dust and a cosmological constant) on all scales. ar