A small cosmological constant from a large number of extra dimensions

TL;DR

This paper proposes a model with extra dimensions in Lanczos-Lovelock gravity where the curvature of a small extra-dimensional sphere cancels out a large vacuum energy, resulting in a small observed cosmological constant.

Contribution

It introduces a mechanism where extra-dimensional curvature cancels vacuum energy, producing a small cosmological constant in a higher-dimensional gravity framework.

Findings

Extra-dimensional curvature cancels large vacuum energy.

Large number of extra dimensions yields an observed small cosmological constant.

The model aligns with observational constraints on the cosmological constant.

Abstract

In this article, we consider the $4+n$ dimensional spacetimes among which one is the four dimensional physical Universe and the other is an n-dimensional sphere with constant radius in the framework of Lanczos-Lovelock gravity. We find that the curvature of extra dimensional sphere contributes a huge but negative energy density provided that its radius is sufficiently small, such as the scale of Planck length. Therefore, the huge positive vacuum energy, i.e. the large positive cosmological constant is exactly cancelled out by the curvature of extra sphere. In the mean time the higher order of Lanczos-Lovelock term contributes an observations-allowed small cosmological constant if the number of extra dimensions is sufficiently large, such as $n\approx{69}$.