Public and private space curvature in Robertson-Walker universes

Abstract

The question is asked: what space curvature would a fundamental observer in an ideal Robertson-Walker universe obtain by direct local spatial measurements, i.e., without reference to the motion pattern of the other galaxies? The answer is that he obtains the curvatureK of his “private” space generated by all the geodesics orthogonal to his world line at the moment in question, and that ∼K is related to the usual curvatureK=k/R ² of the “public” space of galaxies byK=K+H ²/c², whereH is Hubble's parameter.