118725633
Integrable cosmological models with non-minimally coupled scalar fields
We obtain general solutions for some flat Friedmann universes filled with a scalar field in induced gravity models and models including the Hilbert–Einstein curvature term plus a scalar field conformally coupled to gravity. As is well known, these models are connected to minimally coupled models through the combination of a conformal transformation and a transformation of the scalar field. The explicit forms of the self-interaction potentials for six exactly solvable models are presented here. We obtain the general solution for one of the integrable models, namely, the induced gravity model with a power-law potential for the self-interaction of the scalar field. We argue that although being mathematically in a one-to-one correspondence with the solutions in the minimally coupled models, the solutions in the corresponding non-minimally coupled models are physically different. This is because the cosmological evolutions seen by an internal observer connected with the cosmic time can be quite different. The study of a few induced gravity models with particular potentials gives us an explicit example of such a difference.
118914395
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.
122632671
Solutions of nonlocal cosmological equations
A general class of gravitational models driven by a nonlocal scalar field with a linear or quadratic potential is considered. The Ostrogradski representation for nonlocal gravitational models and the way of its localization are proposed. We study the action with an arbitrary analytic function F(□g), which has both simple and double roots. The way of localization allows to find solutions of nonlocal Einstein equations.
15559352
Construction of doubly periodic solutions via the Poincare–Lindstedt method in the case of massless ϕ4 theory
Doubly periodic (periodic both in time and in space) solutions for the Lagrange–Euler equation of the (1+1)-dimensional scalar ϕ4 theory are studied. Provided that the nonlinear term is small, the Poincare–Lindstedt asymptotic method can be used to find asymptotic solutions in the standing wave form. The principal resonance problem, which arises for zero mass, is solved if the leading-order term is taken in the form of Jacobi elliptic function. To obtain this leading-order term the system REDUCE is used.
172508704
New exact solutions for the generalized Henon-Heiles system
118410791
Renormalization-group improved inflationary scalar electrodynamics and SU(5) scenarios confronted with Planck 2013 and BICEP2 results
The possibility to construct inflationary models for the renormalization-group improved potentials corresponding to scalar electrodynamics and to $SU(2)$ and $SU(5)$ models is investigated. In all cases, the tree-level potential, which corresponds to the cosmological constant in the Einstein frame, is seen to be non-suitable for inflation. Rather than adding the Hilbert-Einstein term to the action, quantum corrections to the potential, coming from to the RG-equation, are included. The inflationary scenario is analyzed with unstable de Sitter solutions which correspond to positive values of the coupling function, only. We show that, for the finite $SU(2)$ model and $SU(2)$ gauge model, there are no de Sitter solutions suitable for inflation, unless exit from it occurs according to some weird, non-standard scenarios. Inflation is realized both for scalar electrodynamics and for $SU(5)$ RG-improved potentials, and the corresponding values of the coupling function are seen to be positive. It is shown that, for quite reasonable values of the parameters, the inflationary models obtained both from scalar electrodynamics and from the $SU(5)$ RG-improved potentials, are in good agreement with the most recent observational data coming from the Planck2013 and BICEP2 collaborations.
118194329
STUDY OF RADIO EMISSION FROM EXTENSIVE AIR SHOWERS BY MEANS OF A SYSTEM OF HALF-WAVE DIPOLES IN THE COMPLEX ARRAY OF THE MOSCOW STATE UNIVERSITY.