Geometrical Constraints on the Cosmological Constant

TL;DR

This paper explores how extrinsic curvature influences the cosmological constant, proposing a variable term that decreases rapidly in the early universe, potentially addressing the cosmological constant problem.

Contribution

It introduces a compensation mechanism involving a variable cosmological term linked to extrinsic curvature, offering a novel approach to the cosmological constant problem.

Findings

The variable cosmological constant decreases rapidly during early universe.

Extrinsic curvature behaves as a spin-2 field independent of the metric.

Proposes a hypothesis on extrinsic curvature's behavior to solve the problem.

Abstract

The cosmological constant problem is examined under the assumption that the extrinsic curvature of the space-time contributes to the vacuum. A compensation mechanism based on a variable cosmological term is proposed. Under a suitable hypothesis on the behavior of the extrinsic curvature, we find that an initially large $\Lambda(t)$ rolls down rapidly to zero during the early stages of the universe. Using perturbation analysis, it is shown that such vacuum behaves essentially as a spin-2 field which is independent of the metric.