From satisfying to violating the null energy condition

We construct a theory that admits a time-dependent solution smoothly interpolating between a null energy condition (NEC)-satisfying phase at early times and a NEC-violating phase at late times. We first review earlier attempts to violate the NEC and an argument of Rubakov, presented in [V. A. Rubakov, Phys. Rev. D 88, 044015 (2013)], which forbids the existence of such interpolating solutions in a single-field dilation-invariant theory. We then construct a theory which, in addition to possessing a Poincare-invariant vacuum, does admit such a solution. For a wide range of parameters, perturbations around this solution are at all times stable, comfortably subluminal and weakly coupled. The theory requires us to explicitly break dilation invariance, so it is unlikely that the theory is fully stable under quantum corrections, but we argue that the existence of a healthy interpolating solution is quantum-mechanically robust.