The formative years of symmetric teleparallel gravity

Abstract

Following the introduction of the coincident formulation of General Relativity and the rapid development of $f(Q)$ gravity after 2018, symmetric teleparallel gravity has become one of the most active research areas in modified gravity. As the field has expanded rapidly, some of the conceptual and geometric developments established during its formative years have become less visible in the contemporary literature. This article revisits the early development of symmetric teleparallel gravity between 2004 and 2013 and places these contributions within the broader historical evolution of metric-affine gravity. Particular attention is devoted to Einstein-equivalent field equations, five-parameter quadratic non-metricity Lagrangians and their field equations, the metric formulation in the natural (pure) gauge, exact solutions, and spinor couplings. Several of these developments were originally published in the Turkish Journal of Physics, including the use of the terminology ``symmetric teleparallel gravity'' and its abbreviation ``STPG''. We distinguish these contributions from the earlier symmetric teleparallel formulation of Nester and Yo, who had already used a vanishing connection in a coordinate frame. A short comparison with representative recent work on $f(Q)$ gravity places the historical account in its present context. This letter documents the continuity between the early geometric foundations and subsequent developments of the field.

To appear in Turkish Journal of Physics