  Our main aim is to apply the theory of regularly varying functions to the
asymptotical analysis at infinity of solutions of Friedmann cosmological
equations. A new constant $\Gamma$ is introduced related to the Friedmann
cosmological equations. Determining the values of $\Gamma$ we obtain the
asymptotical behavior of the solutions, i.e. of the expansion scale factor
$a(t)$ of a universe. The instance $\Gamma < 1/4$ is appropriate for both
cases, the spatially flat and open universe, and gives a sufficient and
necessary condition for the solutions to be regularly varying. This property of
Friedmann equations is formulated as the generalized power law principle. From
the theory of regular variation it follows that the solutions under usual
assumptions include a multiplicative term which is a slowly varying function.
