ИСТИНА

Field theories which violate the null energy condition (NEC) are of interest for the solution of the cosmological singularity problem and for models of dark energy with the equation of state parameter w<-1. Generally speaking models that violate the NEC have ghosts, and therefore are unstable and physically unacceptable. However, the possibility of existence of the dark energy with w<-1 on the one hand and the cosmological singularity problem on the other hand, encourage the investigation of models which violate the NEC. Such a possibility can be realized within an effective theory, while the fundamental theory should be stable and admit quantization. From this point of view the NEC violation might be a property of a model that approximates the fundamental theory and describes some particular features of the fundamental theory. The stability of isotropic cosmological solutions in the Bianchi I model is considered. We prove that the stability of isotropic solutions in the Bianchi I metric for positive Hubble parameter follows from their stability in the FRW metric. This result is applied for models inspired by string field theory, which violate the NEC. The stability of kink solutions in the FRW metric is a consequence of the stability of the fixed point the solution tends to. Using the Lyapunov theorem we find conditions, under which fixed points and the corresponding kink solutions are stable. Examples of stable isotropic phantom solutions are presented.