Lorentz violation and cosmological perturbations: a toy brane-world model

We study possible effects of Lorentz violation on the generation of cosmological perturbations in inflation by introducing a simple inflating five-dimensional brane-world set-up with violation of four-dimensional Lorentz invariance at an energy scale kappa. We consider a massless scalar field, meant to mimic perturbations of the inflaton and/ or gravitational field, in this background. At 3-momenta below kappa, there exists a zero mode localized on the brane, whose behaviour coincides with that in four-dimensional theory. In contrast, at 3-momenta above kappa, the localized mode is absent and the physics is entirely five dimensional. As 3-momenta get redshifted, more modes get localized on the brane, a phenomenon analogous to 'mode generation'. We find that for kappa >> H, where H is the inflationary Hubble scale, the spectrum of perturbations coincides with that in four-dimensional theory up to exponentially small corrections. For k < H and time-dependent bulk parameters, the spectrum deviates, possibly strongly, from the flat spectrum even for pure de Sitter inflation.