Models of inflation in a gravitational background with an anisotropic spacetime scaling are studied. The background is a higherdimensional Lifshitz throat with the anisotropy scaling zï¿½?ï¿½1. After the dimensional reduction, the fourdimensional general covariance is explicitly broken to a threedimensional spatial diffeomorphism. As a result the cosmological perturbation theory in this set up with less symmetries have to be formulated. We present the consistent cosmological perturbation theory for this set up. We find that the effective fourdimensional gravitational wave perturbations propagate with a different speed than the higher dimensional gravitational excitations. Depending on the model parameters, for an observer inside the throat, the fourdimensional gravitational wave propagation can be superluminal. We also find that the Bardeen potential and the Newtonian potential are different. This can have interesting observational consequences for lensing and CMB fluctuations. Furthermore, we show that at the linearized level the inflaton field excitations vanish.
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