  We consider trapped inflation in a higher dimensional field space: particle
production at a dense distribution of extra species points leads to a terminal
velocity at which inflation can be driven in steep potentials. We compute an
additional, nearly scale invariant contribution to the power-spectrum, caused
by back-scattering of the continuously produced particles. Since this
contribution has a blue tilt, it has to be sub-dominant, leading to an upper
bound on the coupling constant between the inflatons and the extra species
particles. The remaining allowed parameter space is narrow.
