Stability of de Sitter Solutions in Non-local Cosmological Models

A non-local gravity model, which includes a function $f(\Box^{-1} R)$, where $\Box$ is the d'Alembert operator, is considered. For the model with an exponential $f(\Box^{-1} R)$ de Sitter solutions are explored, without any restrictions on the parameters. Using Hubble-normalized variables, the stability of the de Sitter solutions is investigated, with respect to perturbations in the Bianchi I metric, in the case of zero cosmological constant, and sufficient conditions for stability are obtained.Comment: 10 pages, has been published in the proceedings of the XXth International Workshop on High Energy Physics and Quantum Field Theory (QFTHEP'2011), http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=13

Generalization of cosmological attractor approach to Einstein-Gauss-Bonnet gravity

We construct models with the Gauss-Bonnet term multiplied to a function of the scalar field leading to inflationary scenario. The consideration is related with the slow-roll approximation. The cosmological attractor approach gives the spectral index of scalar perturbations which is in a good agreement with modern observation and allows variability for tensor-to-scalar ratio. We reconstruct models with variability of parameters which allow to reproduce cosmological attractor predictions for inflationary parameters in the leading order of $1/N$ approximation in the Einstein-Gauss-Bonnet gravity

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