Backreaction and the rolling tachyon -- an effective action point of view

We compute the decay of an unstable D9 brane in type IIA string theory including backreaction effects using an effective field theory approach. The open string tachyon on the brane is coupled consistently to the space-time metric, the dilaton and the RR 9-form. The purpose of this note is to address the fate of the open string energy density, which remains constant if no interaction with the closed string modes is included. Our computations show that taking only into account the coupling to the massless closed strings the total energy stored in the open string sector vanishes asymptotically, independently how small one chooses g_s. We find also the large time behaviour of the fields in the Einstein and string frames.