Evolving extrinsic curvature and the cosmological constant problem

TL;DR

This paper explores how evolving extrinsic curvature in FLRW cosmology can address the cosmological constant problem by dynamically compensating vacuum energy effects, leading to an observable upper bound.

Contribution

It introduces a dynamical model of extrinsic curvature derived from an Einstein-Hilbert-like principle that explains the cosmological constant problem.

Findings

Extrinsic curvature acts as a dynamical quantity evolving over time.

The model provides an upper bound for the cosmological constant consistent with observations.

Extrinsic curvature compensates for differences between vacuum energy and the cosmological constant.

Abstract

The concept of smooth deformation of Riemannian manifolds associated with the extrinsic curvature is explained and applied to the FLRW cosmology. We show that such deformation can be derived from Einstein-Hilbert-like dynamical principle producing an observable effect in the sense of Noether. As a result, we notice on how the extrinsic curvature compensates both quantitative and qualitative difference between the cosmological constant $ \Lambda$ and the vacuum energy $\rho_{vac}$ obtaining the observed upper bound for the cosmological constant problem at electroweak scale. The topological characteristics of the extrinsic curvature are discussed showing that the produced extrinsic scalar curvature is an evolving dynamical quantity.