A positive cosmological constant as a geometrical artifact

TL;DR

This paper explores how a positive cosmological constant in lower-dimensional spacetimes can be understood as a geometric feature arising from the properties of a higher-dimensional bulk spacetime with a homothetic vector field, revisiting Kaluza-Klein compactification.

Contribution

It demonstrates that the positive cosmological constant can be interpreted as a geometrical artifact linked to the homothetic structure of the higher-dimensional bulk spacetime.

Findings

Identifies the origin of a positive cosmological constant as a homothetic factor.

Shows the role of homothetic vector fields in higher-dimensional geometries.

Provides a geometric interpretation of late-time cosmological acceleration.

Abstract

We revisit the classical mechanism to produce $d-$dimensional spacetimes via Kaluza-Klein compactification. We made the assumption that the $\left(d+1\right) -$dimensional bulk geometry $\mathcal{M}$ admits a Homothetic Vector Field (HVF) $\mathbf{H}$ relaxing the existence of a zero i.e. $\mathbf{H}\neq 0$ holds on $\mathcal{M}$ and the homothetic bivector $F_{ab}(\mathbf{H})=0$. Under these circumstances we identify the origin of a positive cosmological constant in the $d-$dimensional spacetime as the homothetic factor representing a geometrical artifact of late time state of the $\left( d+1\right) -$dimensional bulk spacetime.