Problems in Size Expansion Analysis based on Hypothetical Relationships between Scale Factor, Exponential Function and Bondi K–FactorProblems in Size Expansion Analysis based on Hypothetical Relationships between Scale Factor, Exponential Function and Bondi K–FactorAA00697606
Exponential function is used not only for the basic growth analysis of the individual plant or animal in animal agriculture but also for the space expansion analysis in cosmology. This study was designed to investigate the problems in the size expansion analysis of the toy space model based on the hypothetical relationships between scale factor, exponential function and Bondi K–factor. Problems (A) ~ (E) were shown. (A) The toy space model using Bondi K–factor was related to the Minkowski space (flat space–time), which was different from the standard model of cosmic expansion based on the FLRW metric. (B) The toy space model was related to the relativistic Doppler redshift, but not to the cosmological redshift that was used in the standard model. (C) Even if Bondi K–factor was hypothetically and forcedly related to the cosmic scale factor through exponential function, the relativistic Doppler redshift merely gave a very poor approximation to the cosmological redshift. (D) The rapid but decelerated expansion at the early stage of the toy space model was not consistent with the accelerated expansion of the inflationary theory. (E) The toy space model did not give the information on the energy distribution of the universe (baryonic matter, dark matter and dark energy), though this toy model gave a mathematical curve composed of early rapid expansion in decelerated expansion, inflection point and accelerated expansion. In conclusion, this study showed that the toy space model using Bondi K–factor had various problems when compared with the standard model of cosmic expansion.