  We investigate the effects of scale-free model on cosmology, providing, in
this way, a statistical background in the framework of general relativity. In
order to discuss properties and time evolution of some relevant universe
dynamical parameters (cosmographic parameters), such as $H(t)$ (Hubble
parameter), $q(t)$ (deceleration parameter), $j(t)$ (jerk parameter) and $s(t)$
(snap parameter), which are well re-defined in the framework of scale-free
model, we analyze a comparison between WMAP data. Hence the basic purpose of
the work is to consider this statistical interpretation of mass distribution of
universe, in order to have a mass density $\rho$ dynamics, not inferred from
Friedmann equations, via scale factor $a(t)$. This model, indeed, has been used
also to explain a possible origin and a viable explanation of cosmological
constant, which assumes a statistical interpretation without the presence of
extended theories of gravity; hence the problem of dark energy could be
revisited in the context of a classical probability distribution of mass, which
is, in particular, for the scale-free model, $P(k)\sim k^{-\gamma}$, with
$2<\gamma<3$. The $\Lambda$CDM model becomes, with these considerations, a
consequence of the particular statistics together with the use of general
relativity.
