Higher Dimensional Dark Energy Investigation with Variable $\Lambda$ and $G$

TL;DR

This paper explores the implications of time-varying cosmological constant and gravitational constant in higher dimensions, addressing key cosmological issues like the universe's age, G's variation, and expansion nature.

Contribution

It introduces a phenomenological model linking variable mbda and G in higher dimensions using Zeldovich's relation, analyzing their cosmological effects.

Findings

Addressed the age problem of the universe.

Analyzed the variation of G over time.

Explored the nature of cosmic expansion.

Abstract

Time variable $\Lambda$ and $G$ are studied here under a phenomenological model of $\Lambda$ through an ($n+2$) dimensional analysis. The relation of Zeldovich (1968) $|\Lambda| = 8\pi G^2m_p^6/h^4$ between $\Lambda$ and $G$ is employed here, where $m_p$ is the proton mass and $h$ is Planck's constant. In the present investigation some key issues of modern cosmology, viz. the age problem, the amount of variation of $G$ and the nature of expansion of the Universe have been addressed.