Non-Riemannian geometry: towards new avenues for the physics of modified gravity

TL;DR

This paper explores non-Riemannian geometry, specifically metric-affine theories, as a novel approach to modified gravity, drawing analogies with crystalline structures and discussing recent applications in gravitational physics.

Contribution

It introduces the use of metric-affine geometry in modified gravity theories and reviews recent developments and applications by the authors.

Findings

Non-Riemannian geometry offers new phenomenology for gravity.

Analogies with crystalline defects provide insights into gravitational phenomena.

Recent applications demonstrate the formalism's potential in gravitational physics.

Abstract

Less explored than their metric (Riemannian) counterparts, metric-affine (or Palatini) theories bring an unexpected phenomenology for gravitational physics beyond General Relativity. Lessons of crystalline structures, where the presence of defects in their microstructure requires the use of non-Riemannian geometry for the proper description of their properties in the macroscopic continuum level, are discussed. In this analogy, concepts such as wormholes and geons play a fundamental role. Applications of the metric-affine formalism developed by the authors in the last three years are reviewed.