Evolving extrinsic curvature and the cosmological constant problem

The concept of smooth deformation of Riemannian manifolds associated with the extrinsic curvature is explained and applied to the Friedmann–Lemaître–Robertson–Walker cosmology. We show that such deformation can be derived from the Einstein–Hilbert-like dynamical principle may produce an observable effect in the sense of Noether. As a result, we show how the extrinsic curvature compensates both quantitative and qualitative differences between the cosmological constant Λ 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. (paper)