Cosmology with the cosmic rest frame

We assume a one-to-one correspondence between comoving coordinates and the cosmic rest frame in a spherically symmetric inhomogeneous universe. This strongly restricts the solutions of Einstein's equations: (i) The pressure must be zero. (ii) The metric does not depend on the radial coordinate, the FLRW cosmology is excluded (strong homogeneity). (iii) The unique solution corresponds to the Datt-Ruban solution. Beside the Hubble constant it contains one free constant of integration which can be chosen in order to represent the measured Hubble diagram without using a cosmological constant.