# How well is our universe described by an FLRW model?

### Abstract

Extremely well! In the ΛCDM model, the spacetime metric, $g_{ab}$, 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 $g_{ab}$ 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—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(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. Our results thereby provide strong justification for the mathematical consistency and validity of the ΛCDM model within the context of general relativistic cosmology.

Publication
Class. Quant. Grav. 31, 234003
##### Stephen R. Green
###### Nottingham Research Fellow

I am a theoretical physicist studying gravitational waves, based at the University of Nottingham. My main interests are in black hole perturbation theory and applying probabilistic machine-learning methods to analyze LIGO data.