Gravity Without Spacetime express
Gravity is usually explained through the curvature of spacetime. Massive bodies press it down like a bowling ball on a stretched rubber sheet. But this approach has two lesser-known twins. In one, gravity arises from torsion (twisting) of spacetime; in the other, from its non-metricity (when lengths and angles change during transport). All three variants yield the same Einstein equations and are called the 'Geometric Trinity of Gravity.'
The authors of the article asked: what was there before spacetime acquired one of these three geometric forms? They proposed a pre-geometric theory — a kind of 'soup' for spacetime. In this soup, there is no metric (a way to measure distances) and no familiar geometry. There are only fields and symmetries, similar to those in Yang–Mills theory. Then, as in the Higgs mechanism, the symmetry spontaneously breaks.
As a result, an effective metric 'precipitates' out of the soup — the very spacetime we live in. Importantly, depending on the choice of gauge (a way to fix extra degrees of freedom), this spacetime can turn out to be curved, twisted, or non-metric. Thus, one and the same deep theory gives rise to all three variants of the Geometric Trinity. It turns out that debates about which geometry is 'more correct' lose their meaning: they are simply different facets of the same whole.
Original abstract
as written by the authors arXiv:2606.17580
The so-called Geometric Trinity of Gravity is based on three distinct geometric features of spacetime, i.e.\ curvature, torsion and non-metricity, which give rise to equivalent dynamics for General Relativity (GR), Teleparallel Equivalent of General Relativity (TEGR) and Symmetric Teleparallel Equivalent of General Relativity (STEGR). Pre-geometric gravity, on the other hand, offers a unifying framework from which all metric-affine theories can emerge. Starting from a gauge formulation \textit{\`a la} Yang--Mills with a Higgs-like field, a mechanism of spontaneous symmetry breaking can give rise to an effective metric as well as to the classical dynamics of the gravitational field. In particular, the emergence of gravity in the spontaneously broken phase is shown to be consistent with all the different formulations of the Geometric Trinity of Gravity, in terms both of actions and of gauge choices for the affine connection. This general result is achieved by deriving and analysing suitable expressions in the unbroken phase for pre-geometric actions and for pre-geometric gauge-fixing conditions respectively.
The idea of describing gravity through the torsion of spacetime dates back to Einstein's attempts to unify gravity with electromagnetism in the 1920s.
In Greg Egan's novel 'Schild's Ladder', physicists explore a universe where the very concept of spacetime emerges from more fundamental mathematical structures.