Cosmographic Connection Between Cosmological And Planck Scales: The Barrow-Tsallis Entropy

TL;DR

This paper explores the connection between quantum gravitational effects and nonextensive thermodynamics in cosmology, using Barrow--Tsallis entropy to relate microscopic quantum foam parameters to macroscopic universe evolution.

Contribution

It introduces a method to relate quantum foam parameters with nonextensive effects and applies fractional derivatives to model late universe evolution.

Findings

Established an exact relationship between quantum foam and nonextensive parameters.

Evaluated the feasibility of fractional derivatives in late universe modeling.

Found that uncertainties depend solely on cosmographic parameter uncertainties.

Abstract

One of the fundamental challenges of quantum gravity is to understand how the microscopic degrees of freedom of the cosmological horizon shape the evolution of the Universe. One possible approach to this problem is based on the Barrow--Tsallis entropy. This entropy accounts for both quantum gravitational effects and the nonextensive effects inherent in any long-range interaction. Using a general method we developed for finding the parameters of cosmological models, we discovered a relationship between the parameter describing the microscopic structure of quantum foam and the parameter associated with macroscopic nonextensive effects. We also used our method for finding the parameters of cosmological models to evaluate the feasibility of using fractional derivatives to describe the late evolution of the Universe. The resulting relationships are exact. Therefore, the uncertainty in the relationship between the model parameters depends only on the current uncertainty in the values of the cosmographic parameters.