Crystal clear lessons on the microstructure of space-time and modified gravity

TL;DR

This paper explores how microscopic structures like wormholes in space-time could lead to effective metric-affine geometries, using analogies from crystal defects, and discusses implications for modified gravity theories.

Contribution

It introduces a model linking microscopic wormholes to metric-affine geometry and shows Einstein's equations emerge as an attractor in this framework, bridging solid state physics and gravity.

Findings

Wormhole formation is possible in metric-affine scenarios.

Einstein's equations with a cosmological constant emerge as an attractor.

Solid state physics analogies provide insights into microstructure of space-time.

Abstract

We argue that a microscopic structure for space-time such as that expected in a quantum foam scenario, in which microscopic wormholes and other topological structures should play a relevant role, might lead to an effective metric-affine geometry at larger scales. This idea is supported by the role that microscopic defects play in crystalline structures. With an explicit model we show that wormhole formation is possible in a metric-affine scenario, where the wormhole and the matter fields play a role analogous to that of defects in crystals. We also point out that in metric-affine geometries Einstein's equations with an effective cosmological constant appear as an attractor in the vacuum limit for a vast family of theories of gravity. This illustrates how lessons from solid state physics can be useful in unveiling the properties of the microcosmos and defining new avenues for modified theories of gravity.