$5D$ Solutions to $\mathrm{\Lambda }$CDM Universe Derived from Global Brane Model

An exact solution of brane universe is studied and the result indicates that Friedmann equations on the brane are modified with an extra term. This term can play the role of dark energy and make the universe accelerate. In order to derive the $\mathrm{\Lambda }$CDM Universe from this global brane model, the new solutions are obtained to describe the $5D$ manifold.