In this paper, we will use a BIonic solution for analyzing the holographic cosmology. A BIonic solution is a configuration of a D3-brane and an anti-D3-brane connected by a wormhole, and holographic cosmology is a recent proposal to explain cosmic expansion by using the holographic principle. In our model, a BIonic configuration will be produced by the transition of fundamental black strings. The formation of a BIonic configuration will cause inflation. As the D3-brane moves away from the anti-D3-brane, the wormhole will get annihilated, and the inflation will end with the annihilation of this wormhole. However, it is possible for a D3-brane to collide with an anti-D3-brane. Such a collision will occur if the distance between the D3-brane and the anti-D3-brane reduces, and this will create tachyonic states. We will demonstrate that these tachyonic states will lead to the formation of a new wormhole, and this will cause acceleration of the universe before such a collision.