Low energy effective action for Hořava-Witten cosmology

As a supersymmetric extension of the Randall-Sundrum model, we consider a 5-dimensional Hořava-Witten type theory and derive its low energy effective action. The model we consider is a two-brane system with a bulk scalar field satisfying the Bogomol'nyi-Prasad-Sommerfield (BPS) condition. We solve the bulk equations of motion using a gradient expansion method, and substitute the solution into the original action to get the 4-dimensional effective action. The resultant effective theory can be cast into the form of Einstein gravity coupled with two scalar fields, one arising from the radion, the degree of freedom of the interbrane distance, and the other from the bulk scalar field. We also clarify the relation between our analysis and the moduli approximation.