Singularities in particle-like description of FRW cosmology

Abstract

In this paper, we apply the method of reducing the dynamics of FRW cosmological models with a 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 make themselves 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 mimic 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 that the general form of the model contains matter and some kind of dark energy which is parameterised by the potential. We distinguish singularities (by an ansatz involving the Lagrangian) of the pole type with the inflation and demonstrate that such a singularity can appear in the past.

Recent Advances in Cosmological Singularities

“…[130] discussed how w-singularities can occur in interacting dark energy models (the background cosmology in this case was still general relativistic, and the continuity equation had its usual form), while [131] showed how varying Chaplygin gas models can also have w-singularities. The occurrence of w-singularities in various other contexts has also been discussed in [91,[132][133][134][135]. Hence, while Type V singularities deal primarily with a more indirect cosmological parameter, they by no means diminish their cosmological importance and they do appear in a variety of cosmological expansion scenarios.…”

Determinants of Financial Inclusion of Urban Women: Evidence from Ahmedabad, India

“…The occurrence of w-singularities in various other contexts has also been discussed in [103,[144][145][146][147]. Hence while type V singularities deal primarily with a more indirect cosmological parameter, it by no means diminishes its cosmological importance and it does appear in a variety of cosmological expansion scenarios.…”