Narrow Results

In this paper, the formation of cylindrical wormhole during evolution of manifolds is studied. It is shown that this type of wormholes may be produced at two stages and then disappeared very fast at the third stage. First, one $N$-dimensional is formed by joining point-like manifolds. Then, this manifold is torn and two child manifolds plus one Chern–Simons manifold appeared. Our universe is born on one of the child manifolds and connected to the other one by Chern–Simons manifold. At the third stage, this Chern–Simons manifold-which plays the role of cylindrical wormhole, dissolves into universes and gives its energy to them and causes inflation. Thus, the Chern–Simons cylindrical wormhole is unstable and dissolves in our four-dimensional universes and another universe very fast.

Recently, the role of energy conditions in $f(R)$-cosmology has been investigated. We generalize these results to BIonic systems in accelerating systems and show that the energy conditions can be changed in this system. We show that $f(R)$-gravity produces a wormhole between two universes and forms a BIonic system. On the other hand, the acceleration creates two regions in the Rindler space-time which BIon in each region acts reverse to other in another region. This means that by the expansion of universes of the BIon in one region, universes of another BIon in other regions contract. Also, in this model, by increasing the order of curvatures in $f(R)$-gravity, the energy and the entropy of system in one region increases and in other region decreases. Amount of this growth or decrease in the energy depends on the acceleration of universes. Finally, by calculating the dark energy equation of state, we observe that one universe enters to phantom phase and goes toward the big rip singularity and another goes out of phantom state.