Espaço cósmico emergente, considerações da teoria de MOND e da termoestatística não-extensiva

Abstract

An old quest of theoretical physics is to find a way such that hte general relativity equations can be written in terms of thermodynamical state equations. Since then, there are new conjectures to fathom gravitation from another point of view. In this way we can finally accept that the gravitational field is not an underlying or emergent field, based on the knowledge of relativity, black holes thermodynamics and different statistical formalisms. An important question that is part ofthis so-called gravity/thermostatistical correspondence is if the holographic surface could be well defined from a massive source, for the non-relativistic case. Since then, it is relevant to understand better the role of the holographic surface concerning the gravity concept, In this thesis, we used Verlinde's formalism and the Padmanabahn proposition to obtain the lowest quantum correction relative to the gravitational acceleration and, in this way, to obtain a modified gravitation theory, by considering the non-zero difference between the matter degrees of freedom (dark energy) and the holographic surface. In this scenario we have analyzed the de Sitter pure Universe's conditions as well as the current asymptotic ,ode, through the holographic principle. This analysis was carried out also by using the non-extensive thermostatistics. By using this result we have analyzed the entropic indice concerning the cosmic holographic analysis