We study dynamics of non-minimally coupled scalar field cosmological models with Higgs-like potentials and a negative cosmological constant. In these models the inflationary stage of the Universe evolution changes into a quasi-cyclic stage of the Uni
verse evolution with oscillation behaviour of the Hubble parameter from positive to negative values. Depending on the initial conditions the Hubble parameter can perform either one or several cycles before to become negative forever.
Simple analytic solution to cubic Neveu-Schwarz String Field Theory including the $GSO(-)$ sector is presented. This solution is an analog of the Erler-Schnabl solution for bosonic case and one of the authors solution for the pure $GSO(+)$ case. Gaug
e transformations of the new solution to others known solutions for the $NS$ string tachyon condensation are constructed explicitly. This gauge equivalence manifestly supports the early observed fact that these solutions have the same value of the action density.
Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of non-polynomial and cubic string field theories are discussed. To have a possibility to deal with both GSO(+) and GSO(-) sectors in
the uniform way a matrix formulation for the NS fermionic SFT is used. In constructions of analytical solutions to open string field theories truncated pure gauge configurations parameterized by wedge states play an essential role. The matrix form of this parametrization for the NS fermionic SFT is presented. Using the cubic open superstring field theory as an example we demonstrate explicitly that for the large parameter of the perturbation expansion these truncated pure gauge configurations give divergent contributions to the equation of motion on the subspace of the wedge states. The perturbation expansion is cured by adding extra terms that are nothing but the terms necessary for the equation of motion contracted with the solution itself to be satisfied.
In constructions of analytical solutions to open string field theories pure gauge configurations parameterized by wedge states play an essential role. These pure gauge configurations are constructed as perturbation expansions and to guaranty that the
se configurations are asymptotical solutions to equations of motions one needs to study convergence of the perturbation expansions. We demonstrate that for the large parameter of the perturbation expansion these pure gauge truncated configurations give divergent contributions to the equation of motion on the subspace of the wedge states. We perform this demonstration numerically for the pure gauge configurations related to tachyon solutions for the bosonic and the NS fermionic SFT. By the numerical calculations we also show that the perturbation expansions are cured by adding extra terms. These terms are nothing but the terms necessary to make valued the Sen conjectures.
The descent relations between string field theory (SFT) vertices are characteristic relations of the operator formulation of SFT and they provide self-consistency of this theory. The descent relations <V_2|V_1> and <V_3|V_1> in the NS fermionic strin
g field theory in the kappa and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.
