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On the basis of an assumption of inter-conversion of matter and dark energy, a theoretical model

We have considered the modified and the extended holographic Ricci dark energy models (MHRDE and EHRDE) in fractal universe. We have assumed a time-like fractal profile V = − , where = 4(1 − ). We have reconstructed the Hubble parameter , the energy density, the equations of state parameter , and the deceleration parameter for both MHRDE and EHRDE.

In the present study, the individual growth process of an organism has been shown with the help of a mathematical model. The surplus energy production rate, i.e. intake rate minus metabolic cost, plays a crucial role in controlling the growth rate. Considering the existence of an optimum mass, which maximizes the surplus energy, it has been found that the scaling exponent for the metabolic cost has to be greater than the exponent for the intake rate. On the basis of the consideration that the system always generates some surplus energy, a relationship among the empirical constants has been established. The growth is found to continue with an ever decreasing rate. When the system attains its optimum mass, the growth rate is found to be the maximum. The mass variation with time has been graphically shown using the expression obtained by solving a differential equation involving surplus energy. Using figures, the dependence of mass variation upon various scaling parameters, has been thoroughly discussed. As mass increases, the surplus energy production rate per unit mass is found to decrease and this may be the probable reason for the smaller number of organisms with larger mass. As the scaling exponent regarding intake increases, the maximum attainable mass increases along with an increase in the time required for its attainment.