arXiv:1403.7452v1 [gr-qc] 28 Mar 2014 Chiral Cosmological Models: Dark Sector Fields Description Chervon S.V. Laboratory of Gravitation, Cosmology, Astrophysics, Ilya Ulyanov State Pedagogical University, Ulyanovsk 432700, Russia Abstract. The present review is devoted to a Chiral Cosmological Model as the self-gravitating nonlinear sigma model with the potential of (self)interactions employed in cosmology. The chiral cosmological model has successive applications in descriptions of the inflationary epoch of the Universe evolution; the present accelerated expansion of the Universe also can be described by the chiral fields multiplet as the dark energy in wide sense. To be more illustrative we are often addressed to the two-component chiral cosmological model. Namely, the two-component chiral cosmological model describing the phantom field with interaction to a canonical scalar field is analyzed in details. New generalized model of quintom character is proposed and exact solutions are founded out. In the review we represented the perturbation theory for chiral cosmological model with the aim to describe the structure formation using the progress achieved in the inflation theory. It was shown that cosmological perturbations from chiral fields can be decomposed for inflaton and the dark sector perturbations. The two- component model is investigated in details, the general solution for shortwave approximation is obtained and analyzed for power law Universe expansion. New issue for understanding the features of Universe evolution is proposed by consideration of the dark sector fields on the inflaton background. The results are illustrated for the solutions in the long-wave approx- imation. 1 Introduction Active investigations of the Early Universe have been originated with understanding of inflationary epoch necessity in the beginning of the 80-s last century. During the decade it became clear strong relation between particle physics (micro-physics) and cosmology (macro-physics) leading to connection of quantum fluctuations in the very early Universe with it large scale structure observed nowadays. Such topics as topological defects, inflation, dark matter, axions and quantum cosmology were studied by many scientists. The questions about physical roots of the Universe expansion source (inflation) or quantum creation of the Universe were discussed in the literature as well (for review see [1]). The discovery of the current acceleration of the Universe at the end of the 20-th century leads to a great number of new theoretical hypothesis to explain this observational fact. We can think over Dark Energy (DE) as the source of modern accelerated expansion of the Universe in a wide sense. The most often DE is represented by the cosmological constant Λ, quintessence as a canonical scalar field with the potential or as the scalar fields coupled to other species of matter/radiation and many others (see, for example, [2]). The general term dark sector fields is used to cover all kinds of DE and Dark Matter (DM). let us study a chiral nonlinear sigma model coupled to gravity in order to make the general framework for dark sector fields and take into account some generalization for multiple-field model. A self-gravitating Nonlinear Sigma Model (NSM) with a potential of (self)interactions has been applied for description of inflationary cosmology [3] and therefore was called The Chiral Inflationary Model. Two years earlier pure kinetic NSM has been considered in cosmology [4], but it could not carry all necessary properties of inflationary period because the equation of state was corresponded to ultra-stiff matter only. The term ”chiral” is considered in the sense of short equivalent to the general chiral NSM with a Rieman- nian metric as a target space in accordance with terminology in the review [5]. Paradoxically, this term has been applied to pure bosonic NSM which has no relation to chiral symmetry because pure bosonic NSM does not contain the spinor fields. Thus the term ”chiral” means that the scalar fields are not free and take values on some nonlinear manifold. 1.1 NSM in Cosmology The chiral cosmological model (CCM) is based on the NSM with the potential of (self)interactions and CCM are generalization for a theory of scalar field singlet which has a lot of applications in cosmology. Therefore it is of interest to consider cosmological applications of the NSM. NSM coupled to the gravitational field has been introduced from the different positions. The 4-dimensional NSM as a generalization from 2-dimensional one can be presented only with coupling to the gravitational field if one wants to have desirable analogy with the gauge theories expressed in existence of instanton and meron solutions. This approach (based on a Riemannian space-time with Euclidian signature) has been realized by De ’Alfaro et al [6]. 1