Richards function in animal growth analysis and Friedmann equation in space expansion analysis
2017
Shimojo, M. (Kyushu University, Fukuoka (Japan). Faculty of Agriculture, Department of Bioresource Sciences, Division of Animal and Marine Bioresource Sciences, Laboratory of Regulation in Metabolism and Behavior)
This study was designed to investigate the analytical concept common to animal growth analysis and space expansion analysis. In addition, the space expansion was investigated using the equivalence principle. Three differential equations for animal growth analysis were obtained from Richards function. Three differential equations for space expansion analysis were Friedmann equations and deceleration parameter. The results obtained were as follows. (I) Three differential equations in both analyses were characterized as follows; (a) the square of the relative growth (or expansion) rate, (b) the relative growth (or expansion) acceleration rate, (c) the equation given by (b)/(a). The analytical concept of differential equation was the same between animal growth analysis and space expansion analysis. This commonness might be ascribed to the mathematical characteristics of the differentiation of exponential function, though the analytical complexity was different between animal growth analysis and space expansion analysis. (II) The increase in the cosmic scale factor in the flat FLRW space-time was related to the decrease in the recession velocity of the illuminant in the Minkowski space-time, an accumulation of equivalence principle suggesting a relationship between the cosmic scale factor and the Lorentz factor. The real expansion of the flat FLRW space-time might be interpreted using the Bondi K-factor elongation of the Minkowski space-time that did not contain the gravity.
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