Inflation in motion: unitarity constraints in effective field theories with (spontaneously) broken Lorentz symmetry

During inflation, there is a preferred reference frame in which the expansion of the background spacetime is spatially isotropic. In contrast to Minkowski spacetime, observables can depend on the velocity of the system with respect to this cosmic rest frame. We derive new constraints from radiative stability and unitarity on effective field theories with such spontaneously broken Lorentz symmetry. In addition to a maximum energy scale, there is now also a critical velocity at which the theory breaks down. The theory therefore has different resolving power in time and in space, and we show that these can only coincide if cubic Lorentz-violating interactions are absent. Applying these bounds to the Effective Field Theory of Inflation, we identify the region of parameter space in which inflation can be both single-field and weakly coupled on subhorizon scales. This can be implemented as a theoretical prior, and we illustrate this explicitly using Planck observational constraints on the primordial bispectrum.