Models of restricted modified theories of gravity and their application in cosmology

In my talk, I will give a short introduction to modified theories of gravity, and then move on to specific modified models of gravity that are the subject of my research. Most of the modified gravity is equivalent to general relativity with some additional degrees of freedom. In our case, these degrees of freedom arise due to the explicit violation of the general covariance by the algebraic connection on the metric coefficients. I am going to discuss the problem of covaritization of such theories, its duality with respect to the well-known models of k-essence and self-gravitating medium, and applications to inflationary cosmology.