Scale-Free model for governing universe dynamics

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.

7 pages, 4 figures

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• Cosmography and constraints on the equation of state of the Universe in various parametrizations
• Updated constraints on $f(\mathcal{R})$ gravity from cosmography
• Entangled states in quantum cosmology and the interpretation of Lambda
• Curvature dark energy reconstruction through different cosmographic distance definitions
• Modeling dark energy through an Ising fluid with network interactions