S. Yu. Vernov

Crossing the w = − 1 barrier in the D3-brane dark energy model

We explore a possibility for the Universe to cross the w=-1 cosmological constant barrier for the dark energy state parameter. We consider the Universe as a slowly decaying D3-brane. The D3-brane dynamics are approximately described by a nonlocal string tachyon interaction and the backreaction of gravity is incorporated in the closed string tachyon dynamics. In a local effective approximation this model contains one phantom component and one usual field with a simple polynomial interaction. To understand cosmological properties of this system we study toy models with the same scalar fields but with modified interactions. These modifications admit polynomial superpotentials. We find restrictions on these interactions under which it is possible to reach w=-1 from below at large time. Explicit solutions with the dark energy state parameter crossing or not crossing the barrier w=-1 at large time are presented.

Exact solution in a string cosmological model

An exact solution to the Friedmann equations with a string inspired phantom scalar matter field is constructed and the absence of the “Big Rip” singularity is shown explicitly. The notable features of the concerned model are a ghost sign of the kinetic term and a special polynomial form of the effective tachyon potential. The constructed solution is stable with respect to small fluctuations of the initial conditions and special deviations of the form of the potential.

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.

Stringy dark energy model with cold dark matter

Abstract Cosmological consequences of adding the cold dark matter (CDM) to the exactly solvable stringy dark energy (DE) model are investigated. The model is motivated by the consideration of our Universe as a slowly decaying D3-brane. The decay of this D-brane is described in the string field theory framework. Stability conditions of the exact solution with respect to small fluctuations of the initial value of the CDM energy density are found. Solutions with large initial value of the CDM energy density attracted by the exact solution without CDM are constructed numerically. In contrast to the ΛCDM model the Hubble parameter in the model is not a monotonic function of time. For specific initial data the DE state parameter w DE is also not monotonic function of time. For these cases there are two separate regions of time where w DE being less than −1 is close to −1.

Construction of exact solutions in two-field cosmological models

A dark energy model with a phantom scalar field, an usual scalar field and the string field theory inspired polynomial potential has been constructed. A two-parameter set of exact solutions to the Friedmann equations has been found. We have constructed such string inspired potential that some exact solutions correspond to the state parameter

Stable exact solutions in cosmological models with two scalar fields

w_{DE}>-1

Renormalization-group improved inflationary scalar electrodynamics and SU(5) scenarios confronted with Planck 2013 and BICEP2 results

at large time, whereas other ones correspond to

Reconstruction of Scalar Potentials in Modified Gravity Models

w_{DE}<-1

Null energy condition violation and classical stability in the Bianchi I metric

at large time. We demonstrate that the superpotential method is very effective to seek new exact solutions. We also present a two-fields model with a polynomial potential and the state parameter, which crosses the cosmological barrier infinitely often.

Localization of the SFT inspired Nonlocal Linear Models and Exact Solutions

We consider the stability of isotropic solutions for two-field models in the Bianchi I metric. We prove that the sufficient conditions for Lyapunov stability in the Friedmann-Robertson-Walker metric ensure the stability under anisotropic perturbations in the Bianchi I metric and also under perturbations of the energy density for cold dark matter. We find sufficient conditions for the Lyapunov stability of isotropic fixed points for the system of Einstein equations. We use the superpotential method to construct stable kink-type solutions and obtain sufficient conditions on the superpotential for the Lyapunov stability of the corresponding exact solutions. We analyze the stability of isotropic kink-type solutions for models related to string field theory.