Is a pole type singularity an alternative to inflation?

TL;DR

This paper explores the possibility that pole-type singularities in cosmological models could serve as alternatives to inflation, using a dynamical systems approach to classify and analyze these singularities.

Contribution

It introduces a method to classify finite scale factor singularities via potential function exponents and shows pole singularities can mimic inflationary epochs.

Findings

Pole singularities can imitate inflation.

Singularities are characterized by critical exponents.

Method applies to models with matter and dark energy.

Abstract

In this paper, we apply a method of reducing the dynamics of FRW cosmological models with the barotropic form of the equation of state to the dynamical system of the Newtonian type to detect the finite scale factor singularities and the finite-time singularities. In this approach all information concerning the dynamics of the system is contained in a diagram of the potential function $V(a)$ of the scale factor. Singularities of the finite scale factor manifest by poles of the potential function. In our approach the different types of singularities are represented by critical exponents in the power-law approximation of the potential. The classification can be given in terms of these exponents. We have found that the pole singularity can mimick an inflation epoch. We demonstrate that the cosmological singularities can be investigated in terms of the critical exponents of the potential function of the cosmological dynamical systems. We assume the general form of the model contains matter and some kind of dark energy which is parameterized by the potential. We distinguish singularities (by ansatz about the Lagrangian) of the pole type with the inflation and demonstrate that such a singularity can appear in the past.