Extra Dimensions, Dual Relation and the Cosmological Constant

TL;DR

This paper explores how extra spatial dimensions influence the cosmological constant and the universe's expansion, deriving effective 4D equations from higher-dimensional models and relating them to observable parameters.

Contribution

It introduces a novel relation connecting extra dimensions with the cosmological constant and Hubble parameter, based on a general n-dimensional manifold framework.

Findings

Derived effective 4D Friedmann equations from higher-dimensional Einstein-Hilbert action.

Established a relation between the Hubble parameter and extra dimensions.

Discussed conditions under which the cosmological constant can be expressed in this framework.

Abstract

We consider a general n dimensional manifold, which is a direct product manifold of $M^4 \times M^{n-4}$ representing our universe and extra spatial dimensions. From Einstein-Hilbert action of the manifold, we deduce effective 4 dimensional Fridemann equations. Matching it with the normal Fridemann equations with the cosmological constant, we give an expression of the cosmological constant, and the expression under different conditions are discussed. Also according to a deduced relation, we reveal a connection between Hubble parameter and extra dimensions. In this regard, we take into account all possible states of extra dimension which are consistent with current experimental result as well.