Abstract
Abstract We considered the f(R) model of gravity with the Yang-Mills field and k-essence in four dimensions, together with the homogeneous, isotropic and flat Friedmann-Robertson-Walker universe. For this model we found equations of motion, a solution for a scale factor, a scalar field, a scalar potential is reconstructed, we studied the slow roll parameters. For the model under consideration, the of slow roll parameters satisfy the region of the inflationary stage. For later times was found the equation of state parameter ω, the deceleration parameter q the value of which corresponds to the accelerated expansion of the universe. Our model allows you to get an accelerated expansion of the universe in the inflationary period. Over time, the field decreases, rolls off slowly, viscosity has a lesser effect, and the universe leaves the inflationary regime, which shows the exponential dynamics of changes in the law of expansion of the universe.