Abstract <p>The equations of cosmological evolution are derived based on a new quasiclassical theory of gravity, which describes the effect of hidden mass or “dark matter.” The dynamic equations correspond to classical mechanics and are Eulerian equations for a dustlike medium. It is shown that taking into account the hidden mass effect leads to Friedmann’s equations for the scale factor of the medium, similar to the equations in general relativity. A comparative analysis of the evolution equations in general relativity and in the new theory is carried out. Based on a qualitative analysis of the Friedmann equations, some possible scenarios of cyclic cosmological evolution are considered, describing all its main stages, including the first and second inflationary stages with an intermediate stage of Friedman expansion.</p>