The Poincare Conjecture and the Cosmological Constant

TL;DR

This paper reviews how deformations in Riemannian geometry relate to gravitation and cosmology, proposing that space-time deformations explain the universe's accelerated expansion without needing a cosmological constant.

Contribution

It introduces a geometric deformation framework that accounts for cosmic acceleration, challenging the traditional cosmological constant approach.

Findings

Deformations of space-time leave observable signatures.

Accelerated expansion explained by space-time deformation.

Dispenses with the need for a cosmological constant.

Abstract

The concept of deformation of Riemannian geometry is reviewed, with applications to gravitation and cosmology. Starting with an analysis of the cosmological constant problem, it is shown that space-times are deformable in the sense of local change of shape. These deformations leave an observable signature in the space-time, characterized by a conserved tensor, associated with a tangent acceleration, defined by the extrinsic curvature of the space-time. In the applications to cosmology, we find that the accelerated expansion of the universe is the observable effect of the deformation, dispensing with the cosmological constant and its problems.