Extensive Composable Entropy for the Analysis of Cosmological Data

Along recent decades, an intensive worldwide research activity is focusing both black holes and cosmos (e. g. the dark-energy phenomenon) on the basis of entropic approaches. The Boltzmann-Gibbs-based Bekenstein-Hawking entropy S₁₇ A/lP² (A area; lP Planck length) systematically plays a crucial theoretical role although it has a serious drawback, namely that it violates the thermodynamic extensivity of spatially-three-dimensional systems. Still, its intriguing area dependence points out the relevance of considering the form W (N) ^N^\;\; (>1; >0), W and N respectively being the total number of microscopic possibilities and the number of components; =1 corresponds to standard Boltzmann-Gibbs (BG) statistical mechanics. For this W (N) asymptotic behavior, we introduce here, on a group-theory basis, the entropic functional S, =k ₈=₁ₖ ₏㶁^1- ^1{} \; (R;\, S₁, ₁=S₁₆-k₈=₁W pᵢ pᵢ). This functional simultaneously is extensive (as required by thermodynamics) and composable (as required for logic consistency), (, ). We further show that (, ) = (1, 2/3) satisfactorily agrees with cosmological data measuring neutrinos, Big Bang nucleosynthesis and the relic abundance of cold dark matter particles, as well as dynamical and geometrical cosmological data sets.