Chiral self-gravitational models: exact solutions and calculation of cosmological parameters

In the presented lecture the chiral self-gravitational models are considered; their inclusion into field theories and construction on the basis of the nonlinear sigma model with the interaction potential. Terminological aspects of the nonlinear sigma model, its connection with harmonic mappings and successes of two-dimensional models as a physical theory of elementary particles are considered. The problem of constructing a four-dimensional chiral model, which has been solved by including the gravitational interaction of bosons, is touched upon. Methods for constructing exact solutions in chiral self-gravitational models are briefly mentioned (with reference to the relevant literature). Considerable interest in modified theories of gravitation is noted, and as an example of such a theory, the theory of gravitation with second order higher derivatives of scalar curvature is considered. The procedure of transition from the theory of gravitation of the form 𝑓(𝑅, (∇𝑅)2,□𝑅) to the theory of gravitation with non-minimal interaction (without higher derivatives). A detailed analysis of the transition from the simplified model 𝑓(𝑅, (∇𝑅)2) to Einstein gravity with scalar fields and then to its representation in the form of a chiral self-gravitational model is also presented. The problem of comparing the predictions of the theory with observational data in the case of several scalar fields in the inflationary model is noted. As an example to solve this problem, it is proposed to construct a singlefield model using a linear relation between the fields. The construction of such a one-field model is presented and the Ivanov-Salopek-Bond method for constructing exact solutions of the equations of cosmological dynamics is described. An algorithm for computing cosmological parameters on the example of a massive scalar field is described. It is noted that it is possible to use connections between fields for matching by masses of particular elementary particles.