I was reading some articles about dark energy and its possible equation of state. I stumbled upon this article https://arxiv.org/abs/1804.02987 which stated that "a dark energy field with
w < -1 is a viable option", "phantom dark energy does not categorically have negative kinetic energy" and "kinetic energy is positive for w≳−1.22, which includes virtually all values of constant w allowed by cosmological data constraints". I'm a bit confused with negative and positive kinetic energy of dark energy, but all sources I've read have stated that Big Rip can happen due to a phantom dark energy field with a negative kinetic energy. Does it not happen if the field has w > -1 but positive kinetic energy? Apologies if I'm misunderstanding something.