This study was conducted to investigate mathematical structures common to animal growth analysis and space expansion analysis. Six particular functions for the growth analysis of the individual animal had a common mathematical structure composed of the respective function and its first and second derivatives. The standard model of the space expansion had a deceleration parameter composed of the scale factor and its first and second derivatives. The results obtained from this study suggested hypotheses (α) ～ (γ). (α) The mathematical structure common to six functions for the animal growth analysis was the same as that of the deceleration parameter for the cosmic expansion analysis, except for the reciprocal form with the negative sign in the latter case. This similarity was based on the symmetry that exponential function showed about the differential calculation at the back of both analyses. (β) There were inflection points both in five functions for the animal growth analysis and in the cosmic expansion history. (γ) If the present size of the space was normalized as '1', then there was a dual interpretation that the cosmic expansion under the general relativity was related to the object recession under the special relativity.