  We study the primordial perturbations generated during a stage of
single-field inflation in Einstein-aether theories. Quantum fluctuations of the
inflaton and aether fields seed long wavelength adiabatic and isocurvature
scalar perturbations, as well as transverse vector perturbations.
Geometrically, the isocurvature mode is the potential for the velocity field of
the aether with respect to matter. For a certain range of parameters, this mode
may lead to a sizable random velocity of the aether within the observable
universe. The adiabatic mode corresponds to curvature perturbations of
co-moving slices (where matter is at rest). In contrast with the standard case,
it has a non-vanishing anisotropic stress on large scales. Scalar and vector
perturbations may leave significant imprints on the cosmic microwave
background. We calculate their primordial spectra, analyze their contributions
to the temperature anisotropies, and formulate some of the phenomenological
constraints that follow from observations. These may be used to further tighten
the existing limits on the parameters for this class of theories. The results
for the scalar sector also apply to the extension of Horava gravity recently
proposed by Blas, Pujolas and Sibiriakov.
