Integrable cosmological models with non-minimal coupling and bounce solutions

We remind the way to obtain integrable models with non-minimally coupled scalar fields. We are interesting to models with bounce solutions and compare bounce solutions in two known integrable models. We show that only one model has a bounce solution that tends to a stable de Sitter solution.Comment: 9 pages, 1 figure, in the proceedings of the 19th International Seminar on High Energy Physics "Quarks-2016

Darboux Transformation of the Green Function for the Dirac Equation with the Generalized Potential

We consider the Darboux transformation of the Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We obtained the Green functions of the transformed Dirac equation with the initial regular boundary conditions. We also construct the formula for the unabridged trace of the difference of the transformed and the initial Green functions of the regular boundary problem of the one-dimensional stationary Dirac equation. We illustrate our findings by the consideration of the Darboux transformation for the Green function of the free particle Dirac equation on an interval.Comment: 14 pages,zip. file: Latex, 1 figure. Typos corrected, the figure replace

F(R)F(R) gravity inflationary model with (R+R0)3/2(R+R_0)^{3/2} term

The proposed inflationary model, which is a one-parametric generalization of the Starobinsky $R+R^2$ model, includes the $(R+3m^2\beta^2)^{3/2}$ term, where the parameter $m$ is the inflaton mass, defined in the same way as in the Starobinsky model, and $\beta$ is a dimensionless constant. Using the conformal transformation and the Einstein frame potential, we obtain the inflationary parameters of the model proposed. The value of the tensor-to-scalar ratio $r$ is bigger than in the Starobinsky model. The considered inflationary model produces a good fit to current observation data.Comment: 11 pages, 2 figure

Construction of inflationary scenarios with the Gauss-Bonnet term and nonminimal coupling

Inflationary models with a scalar field nonminimally coupled both with the Ricci scalar and with the Gauss-Bonnet term are studied. We propose the way of generalization of inflationary scenarios with the Gauss-Bonnet term and a scalar field minimally coupled with the Ricci scalar to the corresponding scenarios with a scalar field nonminimally coupled with the Ricci scalar. Using the effective potential, we construct a set of models with the same values of the scalar spectral index $n_s$ and the amplitude of the scalar perturbations $A_s$ and different values of the tensor-to-scalar ratio $r$.Comment: 11 pages, 5 figures, v2: minor corrections, references are added, to appear in EPJ