Singularities in Inflationary Cosmological Models

Leonardo Fernández-Jambrina

doi:10.3390/universe7120491

Leonardo Fernández-Jambrina

Open Access

https://doi.org/10.3390/universe7120491

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Journal: Universe	Publication Date: Dec 13, 2021
Citations: 1	License type: CC BY 4.0

Affiliation: Universidad Politécnica de Madrid

Abstract

Due to the accelerated expansion of the universe, the possibilities for the formation of singularities has changed from the classical Big Bang and Big Crunch singularities to include a number of new scenarios. In recent papers it has been shown that such singularities may appear in inflationary cosmological models with a fractional power scalar field potential. In this paper we enlarge the analysis of singularities in scalar field cosmological models by the use of generalised power expansions of their Hubble scalars and their scalar fields in order to describe all possible models leading to a singularity, finding other possible cases. Unless a negative scalar field potential is considered, all singularities are weak and of type IV.

Highlights

The formation of singularities is one of the major challenges for general relativity and has lead to plenty of conjectures and results [1] in the field of mathematical relativity
Since these modifications of the standard cosmological model have usually involved violation of at least one energy condition, the main theorems on singularities were not applicable and new types of singular behavior were added to the list, which was enlarged from the original proposal [14] several times [15,16,17]
In the previous section we have identified the scalar field potentials that lead to singularities

Summary

Introduction

The formation of singularities is one of the major challenges for general relativity and has lead to plenty of conjectures and results [1] in the field of mathematical relativity. The discovery that our universe is undergoing accelerated expansion, even presently [2,3,4,5,6,7,8], triggered the search for either new ingredients for the energy content of the universe (dark energy) [9,10] or for modifications of the general theory of gravity that could cope with such a feature [11,12,13] Since these modifications of the standard cosmological model have usually involved violation of at least one energy condition, the main theorems on singularities were not applicable and new types of singular behavior were added to the list, which was enlarged from the original proposal [14] several times [15,16,17]. A final section of conclusions is included, where we show the list of scalar field models that develop singularities, which are seen to be of the weak type IV, unless a negative potential is considered, which allows type II singularities. The list of potentials leading to singularities includes and enlarges the one enclosed in [52,53]

Divergences in the Hubble Parameter and the Scale Factor

Conclusions