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We present a new approach for averaging in general relativity and cosmology.After a short review of the theory originally taken from the equivalenceproblem, we consider two ways how to deal with averaging based on Cartanscalars. We apply the theory for two different LTB models. In the first one,correlation term behaves as a positive cosmological constant, in the secondexample leading correlation term behaves like spatial curvature. We also shownontriviality of averaging for linearized monochromatic gravitational wave.

Averaging in cosmology based on Cartan scalars