Averaging problem in general relativity and cosmology. (English) Zbl 1267.83083

Summary: It is tradition in cosmology to use the homogeneous and isotropic FRW (Friedmann-Robertson-Walker) spacetime. However, the real universe is inhomogeneous and anisotropic on small scales so if we want to retain the FRW approach, we should at least perform some averaging procedure. Because of the nonlinearity of the Einstein field equations, we will in general obtain a nonzero correlation term, which does not necessarily obey the energy condition and so it can mimic the dark energy term. In this article I will try to review different approaches to the averaging problem with the emphasis on cosmology.


83C99 General relativity
83F05 Relativistic cosmology