Modifications of the Hubble Law in Scale-Dependent Cosmology

We study some observational consequences of a recently proposed scale-dependent cosmological model for an inhomogeneous universe. In this model the universe is pictured as being inside a highly dense and rapidly expanding shell with the underdense center. For nearby objects (z≪1), the linear Hubble diagram is shown to remain valid even in this model, which has been demonstrated both analytically and numerically. For large z, we present some numerical results of the redshift luminosity distance relation and the behavior of the mass density as a function of the redshift. It is shown that the Hubble diagram in this model for a locally open universe (Ω(t0, r~0)=0.1) resembles that of the flat Friedmann cosmology. This implies that the study of the Hubble diagram cannot uniquely determine the value of q0 or Ω0. The model also accounts for the fact that Ω0 is an increasing function of the redshift.