Interacting Holographic Dark Energy, Future Singularity and Polytropic Gas Model of Dark Energy in Closed FRW Universe

The present work deals with the accretion of two interacting fluids: dark matter and a hypothetical fluid as the holographic dark energy components onto wormhole in a non-flat FRW universe. First of all, following Cruz et al. (Phys. Lett. B 669, 271 2008), we obtained an exact solution of the Einstein's field equations. Solution describes effectively the actual acceleration and indicates a big rip type future singularity of the universe. After that we have studied the evolution of the mass of wormhole embedded in this FRW universe in order to reproduce a stable universe protected against future-time singularity. We found that the accretion of these dark components leads to a gradual increase of wormhole mass. It is also observed that contrary to the case as shown by Cruz et al. (Phys. Lett. B 669, 271 2008), the big rip singularity of the universe with a divergent Hubble parameter of this dark energy model may be avoided by a big trip. We have established a correspondence between the holographic dark energy with the polytropic gas dark energy model and obtained the potential as well as dynamics of the scalar field which describes the polytropic cosmology.