Nonmetricity formulation of general relativity and its scalar-tensor extension

TL;DR

This paper explores a new class of gravity theories based on nonmetricity, introducing a scalar field coupled to it, and discusses their mathematical structure, differences from other formulations, and cosmological implications like explaining accelerated expansion.

Contribution

It introduces a novel scalar-nonmetricity gravity theory, extending symmetric teleparallel gravity, and analyzes its properties, connections, and potential to explain cosmic acceleration.

Findings

Equations match teleparallel dark energy for flat universe

Differences highlighted between scalar-nonmetricity and scalar-curvature/torsion theories

Potential to model accelerating universe without dark energy

Abstract

Einstein's celebrated theory of gravitation can be presented in three forms: general relativity, teleparallel gravity, and the rarely considered before symmetric teleparallel gravity. Extending the latter, we introduce a new class of theories where a scalar field is coupled nonminimally to nonmetricity $Q$, which here encodes the gravitational effects like curvature $R$ in general relativity or torsion $T$ in teleparallel gravity. We point out the similarities and differences with analogous scalar-curvature and scalar-torsion theories by discussing the field equations, role of connection, conformal transformations, relation to $f(Q)$ theory, and cosmology. The equations for spatially flat universe coincide with those of teleparallel dark energy, thus allowing to explain accelerating expansion.