We consider the stability of isotropic solutions for two-field models in the Bianchi I metric. We prove that the sufficient conditions for Lyapunov stability in the Friedmann-Robertson-Walker metric ensure the stability under anisotropic perturbations in the Bianchi I metric and also under perturbations of the energy density for cold dark matter. We find sufficient conditions for the Lyapunov stability of isotropic fixed points for the system of Einstein equations. We use the superpotential method to construct stable kink-type solutions and obtain sufficient conditions on the superpotential for the Lyapunov stability of the corresponding exact solutions. We analyze the stability of isotropic kink-type solutions for models related to string field 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 a positive Hubble parameter follows from their stability in the Friedmann-Robertson-Walker metric. This result is applied to models inspired by string field theory, which violate the null energy condition. Examples of stable isotropic solutions are presented. We also consider the k-essence model and analyse the stability of solutions of the form Φ(t) = t.
We discuss the classical aspects of dynamics of scalar models with non-positive Higgs potentials in the FRW cosmology. These models appear as effective local models in non-local models related with string field theories. After a suitable field redefinition these models have the form of local Higgs models with a negative extra cosmological term and the total Higgs potential is non-positively defined and has rather small coupling constant. The non-positivity of the potential leads to the fact that on some stage of evolution the expansion mode gives place to the mode of contraction, due to that the stage of reheating is absent. In these models the hard regime of inflation gives place to inflation near the hill top and the area of the slow roll inflation is very small. Meanwhile one can obtain enough e-foldings before the contraction to make the model under consideration admissible to describe inflation. * arefeva@mi.ras.ru † nick bulatov@mail.ru ‡ rgorbachev@mi.ras.ru 1 arXiv:1112.5951v3 [hep-th]
The stability of isotropic cosmological solutions for two-field models in the Bianchi I metrics is considered. We have proved that the sufficient conditions for Lyapunov stability in the Friedmann-Robertson-Walker metric are sufficient for the stability under anisotropic perturbations in the Bianchi I metric as well. The standard way to construct cosmological models with exact solutions in the Friedmann-Robertson-Walker metric is the superpotential method. We have used the superpotential method to construct stable kink-type solutions and obtained conditions on superpotential, which are sufficient conditions for the Lyapunov stability. We analyze the stability of isotropic kink-type solutions for quintom models related to the string field theory.
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