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We present new classes of exact inflationary solutions for a two-component chiral cosmological model with phantom and canonical scalar fields. These solutions are obtained by use of the scale factor in the form corresponding to that exploited in the emergent universe scenario. We outline in detail the method of deriving exact solutions and discuss the potential and kinetic interaction for the model.

We propose the application of the chiral cosmological model (CCM) for the Einstein-Gauss-Bonnet (EGB) theory of gravitation with the aim of finding new models of the Emergent Universe (EmU) scenario. We analysed the EmU supported by two chiral cosmological fields for a spatially flat universe, while we have used three chiral fields when we investigated open and closed universes. To prove the validity of the EmU scenario we fixed the scale factor and found the exact solution by decomposition of EGB equations and solving the chiral field dynamics equation. To this end, we suggested the decomposition of the EGB equations in such a way that the first chiral field is responsible for the Einstein part of the model, while the second field, together with kinetic interaction term, is connected with the Gauss-Bonnet part of the theory. We proved that both fields are phantom ones under this decomposition, and that the model has a solution if the kinetic interaction between the fields equals a constant. We have presented the exact solution in terms of cosmic time. This was done for a spatially flat universe. In the case of open and closed universes we introduced the third chiral field (canonical for closed and phantom for open universe) which is responsible for the EGB and curvature parts. The solution of the third field equation is obtained in quadratures. Thus we have proved that the CCM is able to support EmU scenario in EGB gravity for spatially flat, open and closed universes.

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In this paper, it is shown that the Tensor-Multi-Scalar Theory of Gravity (TMS TG) allows for inflationary solutions for the vacuum case, that is, in the absence of material source. For the two-field TMS TG, solutions are found in the presence of a source in the form of the scalar field in the slow-roll regime, when the gravitational part is given in the Einstein frame, and the action of the non-gravitational (material) field is given in the Jordan frame. In this case, classes of power-law and de Sitter inflation solutions for various potentials of the non-gravitational scalar field are found.