The ground-state of General Relativity, Topological Theories and Dark Matter

TL;DR

This paper explores a modified limit of Einstein's equations that admits a zero metric solution, leading to galaxy rotation curves resembling observations and altered cosmological dynamics.

Contribution

It introduces a novel limit of Einstein equations including a zero metric state, impacting large-scale gravitational behavior and cosmological models.

Findings

Galaxy rotation curves are approximately flat in the model.

Friedman equations gain an additional matter contribution.

The theory exhibits interesting large-scale properties.

Abstract

We suggest a limit of Einstein equations incorporating the state $g_{\mu\nu}=0$ as a solution. The large scale behavior of this theory has interesting properties. For a spherical source, the velocity profile for circular motions is of the form observed in galaxies (approximately flat). For FRW cosmologies, the Friedman equation contains an additional contribution in the matter sector.