Tachyon inflation in an AdS braneworld with back-reaction

We analyze the inflationary scenario based on the tachyon field coupled with the radion of the second Randall-Sundrum model (RSII). The tachyon Lagrangian is derived from the dynamics of a 3-brane moving in the five dimensional bulk. The AdS$_5$ geometry of the bulk is extended to include the radion. Using the Hamiltonian formalism we find four nonlinear field equations supplemented by the modified Friedmann equations of the RSII braneworld cosmology. After a suitable rescaling we reduce the parameters of our model to only one free parameter related to the brane tension and the AdS$_5$ curvature. We solve the equations numerically assuming a reasonably wide range of initial conditions determined by physical considerations. Varying the free parameter and initial conditions we confront our results with the Planck 2015 data.