Inflationary instabilities of Einstein-aether cosmology

Abstract

We examine the consequences of Lorentz violation during slow-roll inflation. We consider a canonical scalar inflaton coupled, through its potential, to the divergence of a fixed-norm timelike vector field, or "aether." The vector is described by Einstein-aether theory, a vector-tensor model of gravitational Lorentz violation. We derive and analyze the cosmological perturbation equations for the metric, inflaton, and aether. If the scale of Lorentz violation is sufficiently small compared to the Planck mass, and the strength of the scalar-aether coupling is suitably large, then the spin-0 and spin-1 perturbations grow exponentially and spoil the inflationary background. The effects of such a coupling on the CMB are too small to be visible to current or near-future CMB experiments; unusually, no isocurvature modes are produced at first order in a perturbative expansion around the aether norm. These results are discussed for both a general potential and a worked example, $m^2 \phi^2$ inflation with a quadratic scalar-aether coupling term.