  We investigate the evolution of the Universe filled with barotropic perfect
fluid in Eddington-inspired Born-Infeld gravity. We consider both the isotropic
and the anisotropic universe. At the early stage when the energy density is
high, the evolution is modified considerably compared with that in general
relativity. For the equation-of-state parameter $w>0$, the initial singularity
is not accompanied as it was discovered for radiation in earlier work. More
interestingly, for pressureless dust ($w=0$), the initial state approaches a de
Sitter state. This fact opens a new possibility of singularity-free nature of
the theory. The anisotropy is mild, and does not develop curvature
singularities in spacetime contrary to general relativity.
