The scale of homogeneity in the R_h= ct universe

Studies of the Universe's transition to smoothness in the context of Lambda cold dark matter (ΛCDM) have all pointed to a transition radius no larger than ∼300 Mpc. These are based on a broad array of tracers for the matter power spectrum, including galaxies, clusters, quasars, the Ly-α forest, and anisotropies in the cosmic microwave background. It is therefore surprising, if not anomalous, to find many structures extending out over scales as large as ∼2 Gpc, roughly an order of magnitude greater than expected. Such a disparity suggests that new physics may be contributing to the formation of large-scale structure, warranting a consideration of the alternative Friedmann-Lemaître-Robertson-Walker cosmology known as the Rh = ct universe. This model has successfully eliminated many other problems in ΛCDM. In this paper, we calculate the fractal (or Hausdorff) dimension in this cosmology as a function of distance, showing a transition to smoothness at ∼2.2 Gpc, fully accommodating all of the giant structures seen thus far. This outcome adds further observational support for Rh = ct over the standard model.