Brane gravity in 4D from Chern–Simons gravity theory

We evaluate a 5-dimensional Randall Sundrum type metric in the Lagrangian of the Einstein–Chern–Simons gravity, and then we derive an action and its corresponding field equations, for a 4-dimensional brane embedded in the 5-dimensional space-time of the theory, which in the limit l → 0 leads to the 4-dimensional general relativity with cosmological constant. An interpretation of the h a matter field present in the Einstein–Chern–Simons gravity action is given. As an application, we find some Friedmann–Lemaitre–Robertson–Walker cosmological solutions that exhibit accelerated behavior.