Wormholes supported by phantom energy from Shan-Chen cosmological fluids

The firm observational confirmation of the late-time acceleration of the universe expansion has proposed a major challenge to the theoretical foundations of cosmology and the explanation of the acceleration mechanism requires the introduction of either a simply cosmological constant, or of a mysterious dark energy component (time dependent or modified gravities), filling the universe and dominating its current expansionary evolution. Universally given that the universe is permeated by a dark energy fluid, therefore, we should also investigate the astrophysical scale properties from the dark energy effects. In the present paper, the exact solutions of spherically-symmetrical Einstein field equations describing wormholes supported by phantom energy that violates the null energy condition from Shan-Chen fluid description are obtained. We have considered the important case that the model parameter $\psi \approx 1$ which corresponds to the saturation effect ", and this regime corresponds to an effective form of asymptotic freedom " for the fluids, but occurring at cosmological rather than subnuclear scales. Then we investigate the allowed range values of the model parameters $g$ and $\omega$ when the space-time metrics describe wormholes and discuss the possible singularities of the solutions, finding that the obtained spacetimes are geodesically complete. Moreover, we construct two traversable wormholes through matching our obtained interior solutions to the exterior Schwarzschild solutions and calculate out the total mass of the wormhole when the wormhole throat size $r\le a$ or $r\le b$, respectively. Finally, we acquire that the surface stress-energy $\sigma$ is zero and the surface tangential pressure $\mathrm{\wp }$ is positive when discussing the surface stresses of the solutions and analyze the traversable wormholes.