Test Matter in a Spacetime with Nonmetricity

TL;DR

This paper explores the role of nonmetricity in metric-affine geometry, examining vacuum solutions and test-matter dynamics, with implications for early universe and high-energy physics.

Contribution

It provides a detailed analysis of nonmetricity effects in metric-affine gravity, including solutions and matter coupling, advancing understanding of non-Riemannian spacetime structures.

Findings

Vacuum solutions exhibit nonmetricity effects.

Test matter with shear degrees of freedom interacts with nonmetricity.

Nonmetricity influences matter motion in early universe scenarios.

Abstract

Examples in which spacetime might become non-Riemannian appear above Planck energies in string theory or, in the very early universe, in the inflationary model. The simplest such geometry is metric-affine geometry, in which {\it nonmetricity} appears as a field strength, side by side with curvature and torsion. In matter, the shear and dilation currents couple to nonmetricity, and they are its sources. After reviewing the equations of motion and the Noether identities, we study two recent vacuum solutions of the metric-affine gauge theory of gravity. We then use the values of the nonmetricity in these solutions to study the motion of the appropriate test-matter. As a Regge-trajectory like hadronic excitation band, the test matter is endowed with shear degrees of freedom and described by a world spinor.