The Construction of Sudden Cosmological Singularities

TL;DR

This paper constructs cosmological solutions with sudden singularities where pressure and acceleration diverge at finite time, yet the universe remains geodesically complete, challenging traditional singularity concepts.

Contribution

It introduces a method using fractional series to construct solutions with sudden singularities in Friedmann-Lemaitre cosmology, revealing new types of finite-time singularities.

Findings

Solutions have finite-time pressure and acceleration singularities

Hubble rate remains finite and regular

Singularities occur without geodesic incompleteness

Abstract

Solutions of the Friedmann-Lemaitre cosmological equations of general relativity have been found with finite-time singularities that are everywhere regular, have regular Hubble expansion rate, and obey the strong-energy conditions but possess pressure and acceleration singularities at finite time that are not associated with geodesic incompleteness. We show how these solutions with sudden singularities can be constructed using fractional series methods and find the limiting form of the equation of state on approach to the singularity.