The Deformable Universe
M. D. Maia, A. J. S. Capistrano, J. S. Alcaniz, Edmundo M. Monte

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.
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