Explaining Phenomenologically Observed Space-time Flatness Requires New Fundamental Scale Physics

TL;DR

This paper proposes new fundamental fields that spontaneously break translational invariance, defining a flat spacetime at the fundamental level, with curvature emerging as an effective theory at larger scales due to defects.

Contribution

It introduces a novel approach with fundamental fields that establish flat spacetime, explaining observed flatness without relying on known physics at Planck scales.

Findings

Fundamental fields can define a flat spacetime with vanishing Riemann tensor.

Curvature arises at larger scales from crystal-like defects in the fundamental fields.

Traditional physics cannot explain flatness from continuum Planck-scale physics alone.

Abstract

The phenomenologically observed flatness - or near flatness - of spacetime cannot be understood as emerging from continuum Planck (or sub-Planck) scales using known physics. Using dimensional arguments it is demonstrated that any immaginable action will lead to Christoffel symbols that are chaotic. We put forward new physics in the form of fundamental fields that spontaneously break translational invariance. Using these new fields as coordinates we define the metric in such a way that the Riemann tensor vanishes identically as a Bianchi identity. Hence the new fundamental fields define a flat space. General relativity with curvature is recovered as an effective theory at larger scales at which crystal defects in the form of disclinations come into play as the sources of curvature.