Inflationary perturbations with Lifshitz scaling
  Instead of Lorentz invariance, gravitational degrees of freedom may obey
Lifshitz scaling at high energies, as it happens in Ho\v{r}ava's proposal for
quantum gravity. We study consequences of this proposal for the spectra of
primordial perturbations generated at inflation. Breaking of 4D diffeomorphism
(Diff) invariance down to the foliation-preserving Diff in Ho\v{r}ava-Lifshitz
(HL) gravity leads to appearance of a scalar degree of freedom in the gravity
sector, khronon, which describes dynamics of the time foliation. One can
naively expect that mixing between inflaton and khronon will jeopardize
conservation of adiabatic perturbations at super Hubble scales. This indeed
happens in the projectable version of the theory. By contrast, we find that in
the non-projectable version of HL gravity, khronon acquires an effective mass
which is much larger than the Hubble scale well before the Hubble crossing time
and decouples from the adiabatic curvature perturbation $\zeta$ sourced by the
inflaton fluctuations. As a result, at super Hubble scales the adiabatic
perturbation $\zeta$ behaves as in an effectively single field system and its
spectrum is conserved in time. Lifshitz scaling is imprinted in the power
spectrum of $\zeta$ through the modified dispersion relation of the inflaton.
We point out violation of the consistency relation between the tensor-to-scalar
ratio and the spectral tilt of primordial gravitational waves and suggest that
it can provide a signal of Lorentz violation in inflationary era.
