AbstractWe push ahead the idea developed in a previous work, that some fraction of the dark matter and the dark energy can be explained as a relativistic effect. The inhomogeneity matter generates gravitational distortions, which are general relativistically retarded. These combine in a magnification effect since the past matter density, which generated the distortion we feel now, is greater than the present one. The non negligible effect on the averaged expansion of the universe contributes

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... h to the estimations of the dark matter and to the dark energy, so that the parameters of the Cosmological Standard Model need some corrections. In this second work we apply the previously developed framework to relativistic models of the universe. It results that one parameter remain free, so that more solutions are possible, as function of inhomogeneity. One of these fully explains the dark energy, but requires more dark matter than the Cosmological Standard Model ($$91\%$$ 91 % of the total matter). Another solution fully explains the dark matter, but requires more dark energy than the Cosmological Standard Model ($$15\%$$ 15 % more). A third noteworthy solution explains a consistent part of the dark matter ($$63\%$$ 63 % of the total matter) and also some of the dark energy ($$4\%$$ 4 % ).