How well is our universe described by an FLRW model?

Understand

Extremely well! In the $\Lambda$CDM model, the spacetime metric, $g_{ab}$, of our universe is approximated by an FLRW metric, $g_{ab}^{(0)}$, 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 $g_{ab}$ are not close to derivatives of $g_{ab}^{(0)}$, 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---within the framework of our approach to treating backreaction---the large matter inhomogeneities that occur on small scales cannot produce significant effects on large scales, so $g_{ab}^{(0)}$ satisfies Einstein's equation with the averaged stress-energy tensor of matter as its source.