Some exact solutions of Friedmann cosmological equation

In this paper we present a number of examples of exact solutions for the Friedmann cosmological equation for metric $F(R)$ gravity model. Emphasis was placed on the possibility of obtaining exact time dependences of the main cosmological physical quantities: scale factor, scalar curvature, Hubble rate and function $F(R)$. For this purpose an ansatz was used to reduce the Friedmann equation to an ordinary differential equation for function $F=F(H^2)$. This made it possible to obtain a number of exact solutions, both already known and new.