Wave function of the radion with a bulk scalar field
  The behaviour of the distance between two branes (the `radion') in a braneworld model with a bulk scalar field is investigated. We show that the BPS conditions of supergravity ensure that the dynamics of the scalar field and the radion are not independent; we derive the four-dimensional effective action, showing that the effective theory is of scalar--tensor nature, coupling the radion to four-dimensional gravity. 
P. Brax, C. van de Bruck, A.C. Davis and C.S. Rhodes