Abstract: | We propose a hyperbolic function form of the Cardassian component in the Cardassian model. Using the repartition of this Cardassian component, we can obtain a non-zero gravitational interaction between the time derivative of Ricci scalar curvature and the baryon/lepton number current in the radiation-dominated universe.Furthermore, the other term that acts like a non-zero cosmological constant would give an accelerated expansion of current universe and the features of this model do not violate our desired requirements. |