The Deformable Universe

TL;DR

This paper explores how smooth deformations of Riemannian manifolds, applied to Einstein's gravity and FLRW cosmology, can produce observable effects like the universe's accelerated expansion.

Contribution

It introduces a novel approach linking Riemannian manifold deformations to observable cosmological phenomena within Einstein's theory.

Findings

Deformations derived from Einstein-Hilbert principle affect spacetime geometry.

Predicted effects are consistent with universe's accelerated expansion.

Observable effects can be measured by four-dimensional observers.

Abstract

The concept of smooth deformations of a Riemannian manifolds, recently evidenced by the solution of the Poincar\'e conjecture, is applied to Einstein's gravitational theory and in particular to the standard FLRW cosmology. We present a brief review of the deformation of Riemannian geometry, showing how such deformations can be derived from the Einstein-Hilbert dynamical principle. We show that such deformations of space-times of general relativity produce observable effects that can be measured by four-dimensional observers. In the case of the FLRW cosmology, one such observable effect is shown to be consistent with the accelerated expansion of the universe.