Notes on f(R) Cosmological Models with Yang-Mills and Scalar Fields

The present study deals with the Friedmann-Robertson-Walker cosmological models of the Yang-Mills fields and f(R) generalization of the Einstein cosmology. We investigate the corresponding relation between f(R) gravity and interacting Yang-Mills and scalar fields. A method of conformal transformation is proposed, which allows to transform a cosmological theory with nonlinearity induced by the Yang-Mills field into f(R) generalization of Einstein's theory. A specific generalization of Einstein theory on the basis of exact solution for the Yang-Mills equation obtained by the author early is presented in explicit form. Moreover, for the f(R) theory we have found the explicit form of potential of induced scalar field, which can be identified with the effective potential of the f(R) cosmology