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We consider modified gravity cosmological models that can be transformed intotwo-field chiral cosmological models by the conformal metric transformation.For the $R^2$ gravity model with an additional scalar field and thecorresponding two-field model with the cosmological constant and nonstandardkinetic part of the action, the general solutions have been obtained in thespatially flat FLRW metric. We analyze the correspondence of the cosmic timesolutions obtained and different possible evolutions of the Hubble parametersin the Einstein and Jordan frames.

Integrable modified gravity cosmological models with an additional scalar field