Emergence of cosmic space, Gauss-Bonnet gravity, MOND theory and nonextensive considerations

TL;DR

This paper explores quantum corrections to gravity, MOND theory, and nonextensive effects within holographic and Gauss-Bonnet gravity frameworks, analyzing their implications in de Sitter universes and higher dimensions.

Contribution

It introduces a novel approach combining Verlinde's formalism, Padmanabhan's prescription, and nonextensive concepts to extend gravitational theories and analyze their physical consequences.

Findings

Derived quantum corrections to gravitational acceleration.

Established a relation between the nonextensive parameter and Gauss-Bonnet coefficient.

Analyzed physical implications in de Sitter universes and higher-dimensional models.

Abstract

In this paper, by using Verlinde's formalism and a modified Padmanabhan's prescription, we have obtained the lowest order quantum correction to the gravitational acceleration and MOND-type theory by considering a nonzero difference between the number of bits of the holographic screen and the number of bits of the holographic screen that satisfy the equipartition theorem (the bulk). We will also carry out an analysis for the pure and an asymptotic (actual) de Sitter Universe considering the holographic principle. We had also used nonextensive concepts into the theory and we accomplished a $N$-dimensional generalization of our results. Some physical consequences of the nonextensive ideas in Gauss-Bonnet (GB) gravity theory were analyzed also. We have obtained the $q$-parameter as a function of the GB coefficient and some physical aspects were discussed.