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Every theory that modifies gravity at cosmological distances and that is notalready ruled out by the Solar system observations must exhibit some nonlinearmechanism that turns off the modification close to a compact matter source.Given this nonlinearity, one might expect such a theory to show a largegravitational backreaction, i.e. an order one influence of the small scaleinhomogeneities on the large scale evolution of the Universe. We argue thatthis is not necessarily the case. If the dominant nonlinear terms in theequations obey a shift symmetry, the averaged effect of the nonlinearities canbe small, although the effect on small scales is large. This happens for DGP(-like) modifications and so called f(G) (or Gauss-Bonnet) models. For bothtype of models the shift symmetry is part of the larger "Galilean" symmetry.

On the cosmological backreaction for large distance modifications of gravity