Renormalization of the long-wavelength solution of Einstein’s equation

Using the renormalization group method, we improve the first order solution of the long-wavelength expansion of the Einstein equation. By assuming that the renormalization group transformation has the property of a Lie group, we can regularize the secular divergence caused by the spatial gradient terms and absorb it into the background seed metric. The solution of the renormalization group equation shows that the renormalized metric describes the behavior of gravitational collapse in the expanding universe qualitatively well.