Lorentz-violating brane worlds and cosmological perturbations

We consider an inflating brane world setup in which 4-dimensional Lorentz invariance is violated at high 3-momentum scale P-LV > H, where H is the inflationary Hubble parameter. We study massless scalar field in this background as a model for cosmological perturbations. Towards the end of inflation, the spectrum has both the standard, 4-dimensional part due to a brane-localized mode, and exotic, bulk-induced contribution. The suppression of the latter is power-law only, (H/P-LV)(alpha), provided that there exists bulk modes with energies omega << H. Contrary to general expectations, the exponent alpha may be smaller than 2, and even smaller than 1, depending on details of the bulk geometry. Furthermore, the overall amplitude of the bulk-induced perturbations is enhanced as compared to the standard part, so the effects due to Lorentz violation may dominate over the standard mechanism even for P-LV >> H.