Spherical Shell Cosmological Model and Uniformity of Cosmic Microwave   Background Radiation
  Considered is spherical shell as a model for visible universe and parameters that such model must have to comply with the observable data. The topology of the model requires that motion of all galaxies and light must be confined inside a spherical shell. Consequently the observable universe cannot be defined as a sphere centered on the observer, rather it is an arc length within the volume of the spherical shell. The radius of the shell is 4.46 $\pm$ 0.06 Gpc, which is for factor $\pi$ smaller than radius of a corresponding 3-sphere. However the event horizon, defined as the arc length inside the shell, has the size of 14.0 $\pm$ 0.2 Gpc, which is in agreement with the observable data. The model predicts, without inflation theory, the isotropy and uniformity of the CMB. It predicts the correct value for the Hubble constant $H_0$ = 67.26 $\pm$ 0.90 km/s/Mpc, the cosmic expansion rate $H(z)$, and the speed of the event horizon in agreement with observations. The theoretical suport for shell model comes from general relativity, curvature of space by mass, and from holographic principle. The model explains the reason for the established discrepancy between the non-covariant version of the holographic principle and the calculated dimensionless entropy $(S/k)$ for the visible universe, which exceeds the entropy of a black hole. The model is in accordance with the distribution of radio sources in space, type Ia data, and data from the Hubble Ultra Deep Field optical and near-infrared survey. 
Branislav Vlahovic
physics.gen-ph