Variable $G$ Correction for Dark Energy Model in Higher Dimensional Cosmology

TL;DR

This paper investigates how a variable gravitational constant G affects the statefinder parameters in higher-dimensional cosmology, considering interactions between dark energy and dark matter, and applying the model to generalized Chaplygin gas.

Contribution

It introduces corrections to statefinder parameters due to variable G in higher-dimensional cosmology, including cases with interacting and non-interacting dark energy and dark matter.

Findings

Derived G-corrections to statefinder parameters in higher dimensions.

Analyzed effects for both interacting and non-interacting dark sectors.

Applied corrections to generalized Chaplygin gas models.

Abstract

In this work, we have considered $N (=4+d)$-dimensional Einstein field equations in which 4-dimensional space-time which is described by a FRW metric and that of the extra $d$-dimensions by an Euclidean metric. We have calculated the corrections to statefinder parameters due to variable gravitational constant $G$ in higher dimensional Cosmology. We have considered two special cases whether dark energy and dark matter interact or not. In a universe where gravitational constant is dynamic, the variable $G$-correction to statefinder parameters is inevitable. The statefinder parameters are also obtained for generalized Chaplygin gas in the effect of the variation of $G$ correction.