Cosmological distances scale. Pt. 12. Confluence analysis, rang inversion and tests for inadequacy

Abstract

The measurement problem of calibration of the cosmological distance scale is considered from the point of view of the conditions of applicability of the regression analysis. It is shown that the rank inversion and statistical heterogeneity of data on supernovae SN Ia, which were used in 1998–1999 to detect the “acceleration of the expansion of the Universe”, and in 2004–2007 – as “extraordinary evidence” of its existence, is the reason for the discrepancy and inconsistency of the obtained estimates of the parameters of the Friedman-Robertson-Walker model. Although the use of tests for inadequacy for models of the cosmological distance scale reduces these negative effects, the fact remains that the cosmological distance scale based on redshift has neither the status of metric nor ordinal.