Negative $\Lambda$ induced by accelerated motion

TL;DR

The paper explores a model where accelerated motion in a higher-dimensional spacetime induces a negative cosmological constant on a brane, linking acceleration to the curvature of the universe in a novel way.

Contribution

It proposes a correlation between acceleration and a noncompact fifth dimension, deriving a negative cosmological constant from the brane's position in the extra dimension.

Findings

The brane's metric is conformally flat with negative cosmological constant.

Proper acceleration is inversely proportional to the fifth dimension coordinate.

Acceleration of observers relates directly to the brane's position in the extra dimension.

Abstract

A correlation between accelerated motion and a noncompact 5th dimension is proposed. The curvature invariants and the stress energy tensor in the bulk depend only on the 5th dimension $w$ and vanish asymptotically while the proper acceleration of a static observer is proportional to $1/w$. The brane (located at $w = w_{0}$) metric is conformally flat (of AdS type) with $\Lambda = -3/w_{0}^{2}$ and the invariant acceleration $a = \sqrt{a^{b}a_{b}} = 1/w_{0}$. Therefore, we assume that a hyperbolic observer with the rest-system acceleration $a$ is embedded in the 5th dimension at $w_{0} = 1/a$.