Scale-free model for governing the universe dynamics

We investigate the effects of scale-free statistics in Friedman-Robertson-Walker cosmology, in a toy model which considers a matter distribution P(k)~k-γ, with 2<γ<3. Then we address the consequences on dynamics by using the kinematical parameters, namely the cosmographic parameters (Visser M., Phys. Rev. D, 78 (2008) 063501), i.e. H(t) (Hubble parameter), q(t) (deceleration parameter), j(t) (jerk parameter) and s(t) (snap parameter) for the so-called cosmographic test (see the paper by Visser). We show that the scale-free additive background seems able to explain the origin of dark energy giving a statistical interpretation of the cosmological overcoming the fine-tuning and the coincidence problems. After this, a consistent comparison with data by a Supernovae Ia test shows that the model behaves well at z1.