Scale-Free model for governing universe dynamics

TL;DR

This paper explores a scale-free statistical model of universe mass distribution within general relativity, analyzing its implications for cosmological parameters and offering an alternative perspective on dark energy and the cosmological constant.

Contribution

It introduces a scale-free statistical framework for universe dynamics that explains cosmological parameters and the cosmological constant without extended gravity theories.

Findings

The model aligns with WMAP data for cosmographic parameters.

It offers a statistical interpretation of dark energy.

The approach reproduces $ m extbf{ extit{ extLambda}CDM}}$ as a consequence of statistical assumptions.

Abstract

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.