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Significant discrepancies in estimates of the Hubble constant are discussed in terms of the measurementproblem of calibrating the cosmological distance scale. It is shown that representing the Freedman–Robertson–Walker problem by a 3rd order Taylor expansion with respect to the criterion of minimal error inthe inadequacy is not optimal in terms of accuracy. An anisotropic 2nd order model based on the Heckmannrepresentation is more accurate. [ABSTRACT FROM AUTHOR]

The data on the type SN Ia supernovae used to confirm the accelerated 'expansion of the universe' in 1998-1999 are analyzed statistically. A substantial statistical anisotropy with respect to declination is found in these data. It is shown that an examination of the relationship between the red shift of SN Ia supernovae and the photometric distance based on these data is not the most plausible hypothesis. An example of the construction of an anisotropic cosmological distance scale is given. [ABSTRACT FROM AUTHOR]

This is a statistical analysis of data on type SN Ia supernovae from which it was concluded during 1998-1999 that the expansion of the universe is accelerating. The hypothesis that there exists a standard value of the red shift in the spectra of type SN Ia supernovae that corresponds to a standard value of the absolute stellar magnitude for distance determinations is examined. [ABSTRACT FROM AUTHOR]

The paradoxes revealed by red shift models during construction of the cosmological distance scale are examined. [ABSTRACT FROM AUTHOR]

A unified scale of cosmological distances from 0.01 to 13.18 billion light years is constructed from the observed red shifts and stellar magnitudes of 440 quasars, radio galaxies, and galaxies in the Local volume based on an interpolation model with a discontinuity of the second kind and Arp-Trumpler correction to the intrinsic red shift. [ABSTRACT FROM AUTHOR]