Abstract
We present a qualitative analysis of chiral cosmological model (CCM) dynamics with two scalar fields in the spatially flat Friedman–Robertson–Walker Universe. The asymptotic behavior of chiral models is investigated based on the characteristics of the critical points of the selfinteraction potential and zeros of the metric components of the chiral space. The classification of critical points of CCMs is proposed. The role of zeros of the metric components of the chiral space in the asymptotic dynamics is analysed. It is shown that such zeros lead to new critical points of the corresponding dynamical systems. Examples of models with different types of zeros of metric components are represented.
Highlights
A Chiral Cosmological Model (CCM) is a self-gravitating nonlinear sigma model (NSM)containing the interaction potential and employed in cosmological spacetimes
The most important conclusion that can be drawn from the performed numerical analysis of the model are that the asymptotic behavior of chiral cosmological models is determined by the minima of the interaction potential
From the analysis of the dynamics of models in which the metric component h22 of the chiral space vanishes at some points, it follows that the presence of these zeros can significantly change the nature of cosmological evolution both with respect to the evolution of fields and with respect to the Hubble parameter
Summary
A Chiral Cosmological Model (CCM) is a self-gravitating nonlinear sigma model (NSM). containing the interaction potential and employed in cosmological spacetimes. In addition to the a priori specified symmetry and reconstruction of the chiral metric and potential from observational data we can mention about another constraint on the CCM characteristic Such constraint can arose when the transition from the gravity theory with higher derivatives in the Jordan frame is made to the Einstein frame with several scalar fields [21]. We note that kinetic interaction between scalar fields were not considered in all these works Another example is the approach outlined in [41], where the features of the evolution of cosmological models were considered from the point of view of their dynamics on the energy plane.
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