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.
118566695
Stable exact cosmological solutions in induced gravity models
We study dynamics of induced gravity cosmological models with the sixth degree polynomial potentials, that have found using the superpotential method. The important property of these models are existence of exact cosmological solutions that tend to fixed points. The stability of these cosmological solutions have been obtained. In particular, we find conditions under which solutions with a non-monotonic Hubble parameter that tend to a fixed point are attractors.
125533559
Nonlocal cosmological models and exact solutions
119152817
On bouncing solutions in non-local gravity
A non-local modified gravity model with an analytical function of the d’Alembert operator, is considered. This model has been recently proposed as a possible way of resolving the singularities problem in cosmology. We present exact bouncing solution, which is simpler compared to the already known one in this model, in the sense it does not require an additional matter to satisfy all gravitational equations.
119703497
Elliptic solutions of the quintic complex one-dimensional Ginzburg–Landau equation
The Conte–Musette method has been modified for the search of only elliptic solutions to systems of differential equations. A key idea of this a prior restriction is to simplify calculations by means of the use of a few Laurent-series solutions instead of one and the use of the residue theorem. The application of this approach to the quintic complex one-dimensional Ginzburg–Landau equation (CGLE5) allows us to find elliptic solutions in the wave form. Restrictions on coefficients, which are necessary conditions for the existence of elliptic solutions for the CGLE5, have been found as well. We demonstrate that to find elliptic solutions the analysis of a system of differential equations is preferable to the analysis of the equivalent single differential equation.
895
Construction of Single-valued Solutions for Nonintegrable Systems with the Help of the Painleve Test
The Painleve test is very useful to construct not only the Laurent-series solutions but also the elliptic and trigonometric ones. Such single-valued functions are solutions of some polynomial first order differential equations. To find the elliptic solutions we transform an initial nonlinear differential equation in a nonlinear algebraic system in parameters of the Laurent-series solutions of the initial equation. The number of unknowns in the obtained nonlinear system does not depend on number of arbitrary coefficients of the used first order equation. In this paper we describe the corresponding algorithm, which has been realized in REDUCE and Maple.
118415722
Multiplicity Distribution of the Particles Produced in Nuclear Interactions of High-Energy Cosmic Rays