Ekaterina Pozdeeva

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.

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

Holographic phase diagram of quark-gluon plasma formed in heavy-ion collisions

SU(2)

Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

and

Interdependence between integrable cosmological models with minimal and non-minimal coupling

SU(5)

HOLOGRAPHIC ESTIMATION OF MULTIPLICITY AND THE COLLISION OF MEMBRANES IN MODIFIED AdS5 SPACES

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

Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities

SU(2)

Stable exact cosmological solutions in induced gravity models

model and

New exactly solvable periodic potentials for the Dirac equation

SU(2)

Explicit Darboux transformations of arbitrary order for generalized time-dependent Schrödinger equations

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