On spacetime geometry above the electroweak symmetry breaking scale

TL;DR

This paper questions the universal assumption of pseudo-Riemannian geometry of spacetime at all scales, proposing it may only emerge after the electroweak phase transition when the geometry acquires the structure needed for massive particle motion.

Contribution

It challenges the standard assumption by suggesting spacetime geometry may only become pseudo-Riemannian after the electroweak symmetry breaking, based on physical motivation.

Findings

Spacetime may not have a full pseudo-Riemannian structure above the electroweak scale.

The emergence of spacetime geometry could be linked to the electroweak phase transition.

The projective structure of spacetime might be necessary for describing massive particles.

Abstract

While it is generally agreed that the nature of spacetime must be drastically different at the Planck scale, it has been a common practice to assume that spacetime is endowed with a full pseudo-Riemannian geometry regardless of the physical fields present or the length scale at which the geometry is probed, and to adopt this assumption in theories of cosmology, particle physics, quantum gravity, etc. Following Einstein's view that the mathematical description of spacetime ought to be physically motivated, we initiate a discussion on the validity of this assumption, and propose that the full pseudo-Riemannian geometry of spacetime could emerge as late as the time of electroweak phase transition when spacetime acquires the projective structure necessary to describe the motions of massive particles.