Resolving Cosmological Singularities

TL;DR

This paper proposes a simple modification to General Relativity that avoids cosmological singularities by introducing limiting curvature, resulting in a universe with a regular bounce and a natural dark matter candidate.

Contribution

It introduces a novel modification to the longitudinal mode of General Relativity that prevents singularities and provides a candidate for dark matter.

Findings

Singularities in Friedmann and Kasner universes are avoided.

The universe undergoes a regular bounce during high curvature.

The modification naturally includes a dark matter candidate.

Abstract

We find a simple modification of the longitudinal mode in General Relativity which incorporates the idea of limiting curvature. In this case the singularities in contracting Friedmann and Kasner universes are avoided, and instead, the universe has a regular bounce which takes place during the time inversely proportional to the square root of the limiting curvature. Away from the bounce, corrections to General Relativity are negligible. In addition the non-singluar modification of General Relativity delivers for free a realistic candidate for Dark Matter.