Abstract
We consider modified gravity cosmological models that can be transformed into two-field chiral cosmological models by the conformal metric transformation. For the R^2 gravity model with an additional scalar field and the corresponding two-field model with the cosmological constant and nonstandard kinetic part of the action, the general solutions have been obtained in the spatially flat FLRW metric. We analyze the correspondence of the cosmic time solutions obtained and different possible evolutions of the Hubble parameters in the Einstein and Jordan frames.
Highlights
Modified gravity models are actively investigated [1,2,3,4,5]
We show that for some modified gravity models the suitable parametric time is the cosmic time in the Einstein frame
We have found general solutions in the cosmic time for the two-field chiral cosmological model
Summary
Modified gravity models are actively investigated [1,2,3,4,5]. An important class of these models that includes F(R) gravity models and models with a nonminimal coupling between the scalar field and the curvature is characterized by the possibility to construct the mathematically equivalent General Relativity models with a scalar field by the conformal metric transformation. The integrability of cosmological models with nonminimal coupling is more apparent, than the integrability of the corresponding models in the Einstein frame [64,65,66] The generalization of this analysis on the case of a few scalar fields is not straightforward, because the conformal transformation of the metric changes the form of kinetic terms of the scalar fields. To find integrable modified gravity models with an additional scalar field it can be useful to study the corresponding chiral cosmological model. We get scalar fields in the analytic form The knowledge of this general solution allows us to get the general solution of the initial modified gravity models with an additional standard or phantom scalar field in the parametric time. 4, we consider the corresponding R2 gravity model with an additional scalar field and obtain its general solution in the cosmic time.
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