Averaging in cosmology based on Cartan scalars

We present a new approach for averaging in general relativity and cosmology. After a short reviewof the theory originally taken from the equivalence problem, we consider two ways of dealing with averaging based on Cartan scalars. We apply the theory for two different Lemaitre-Tolman-Bondi models. In the first one, the correlation term behaves as a positive cosmological constant, in the second example, the leading correlation term behaves like spatial curvature. We also show the non-triviality of averaging for linearized monochromatic gravitational wave.