A supplement to mathematical structure common to animal growth analysis and space expansion analysis
2016
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 conducted to add some explanations to the previous study on the mathematical structure common to animal growth analysis and space expansion analysis. The results obtained were as follows. (A) In the construction of differential equations, the way of combining the Bertalanffy equation with its first and second derivatives in animal growth analysis was the same as the way of combining the Friedmann equations with its first and second derivatives in space expansion analysis. This commonness was related to the feature of differential calculation of exponential function. The animal growth analysis was based on the balance between anabolism and catabolism, and the space expansion analysis was based on the balance between attractive force and repulsive force. Those two phenomena might look like each other. (B) The space expansion was discussed in terms of two different redshifts. There was a duality in the interpretation of space expansion history using cosmic scale factor (cosmological redshift) and toy space model (relativistic Doppler redshift). This might be related to the hypothesis that the flat FLRW space with gravity might look like the Minkowski space without gravity.
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