Bulk scalar field in the braneworld can mimic the 4D inflaton dynamics

Based on the recently proposed scenario of inflation driven by a bulk scalar field in the braneworld of the Randall-Sundrum (RS) type, we investigate the dynamics of a bulk scalar field on the inflating braneworld. We derive the late-time behavior of the bulk scalar field by analyzing the property of the retarded Green function. We find that the late-time behavior is basically dominated by a single (or a pair of) pole(s) in the Green function irrespective of the initial condition and of the signature of m(2)=V-'(phi), where V(phi) is the potential of the bulk scalar field. Including the lowest-order backreaction to the geometry, this late-time behavior can be well approximated by an effective four-dimensional scalar field with m(eff)(2)=m(2)/2. The mapping to the four-dimensional effective theory is given by a simple scaling of the potential with a redefinition of the field. Our result supports the picture that the scenario of inflation driven by a bulk scalar field works in quite a similar way to that in the standard four-dimensional cosmology.