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 $P_{LV} \gg H$, 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 exist bulk modes with energies $\omega \ll H$. 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 $P_{LV} \gg H$.