Gradient instability for w < -1

Abstract

We show that in single scalar field models of the dark energy with equations of state satisfying $w \equiv p / \rho < -1$, the effective Lagrangian for fluctuations about the homogeneous background has a wrong sign spatial kinetic term. In most cases, spatial gradients are ruled out by microwave background observations. The sign of $w+1$ is not connected to the sign of the time derivative kinetic term in the effective Lagrangian.