Distortions of Robertson–Walker metric in perturbative cosmology and interpretation as dark matter and cosmological constant

In the last years, we saw more and more attempts to explain dark matter as a general relativistic effect, at least for some fraction. Following this philosophy, we considered the gravitational distortions due to the inhomogeneous distribution of matter in the universe, which we know from general relativity to be retarded distortions. This provides a magnification effect, since the distortions we feel now depend not on the present matter density, but on the past one, which is greater. The expansion rate of the universe is perturbed as well, in a not negligible way, despite matter inhomogeneities are small, because of the same magnification effect. The deceleration parameter, which is a way to evaluate the quantity of dark matter in the universe, is perturbed in turn, so that the real amount of dark matter is less than what is usually believed.