In this paper we study the cosmological evolution of the universe filled with a perfect fluid in the Eddington-inspired Born-Infeld gravity. Applying an alternative method in which the evolution of the scale factor for this theory is linked to the cosmographic parameters, we obtain a dynamical dark energy solution where the singularity (through a regular bounce or a loitering phase) still can be avoided for $\kappa>0$ with $w>0$. For the range $-1<w<0$, the results lead us to universes that experience an unlimited rate of expansion with finite density. Also, we obtain a possible maximum value of $H=4.338\times10^{ -43}/t_{ \text{ Planck}}$ at the cosmic bounce point.
Categories: gr-qc