The Deformable Universe

Understand

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.