  We discuss a method of calculating the key cosmological parameters on the
basis of a selected scale factor by using exact solutions of the background
equations. We specify the formulas for calculating the power spectrum, the
spectral indices and their ratios, and the ratio of squared amplitudes of
scalar and tensor perturbations. We obtain, for the first time, expressions for
the basic cosmological parameters in terms of the scalar factor value at the
instant of crossing the cosmological horizon. In this case, the cosmological
parameters are calculated for a wide class of exact models. They are compared
with their analogs derived in the slow-rolling approximation.
