Sudden Future Singularities and their observational signatures in Modified Gravity

TL;DR

This paper investigates the existence and observational signatures of Generalized Sudden Future Singularities in quintessence and scalar-tensor models with specific scalar potentials, providing analytical and numerical insights into their strength.

Contribution

It introduces a generalized expansion ansatz for analyzing singularities and extends the analysis to scalar-tensor models, offering new analytical expressions for singularity strength.

Findings

GSFS exist in quintessence models with $V() o ||^n$, $0<n<1$

Analytical expressions for singularity strength in terms of $n$

SFS also occur in scalar-tensor quintessence models with the same potential

Abstract

We verify the existence of Generalized Sudden Future Singularities (GSFS) in quintessence models with scalar field potential of the form $V(\phi)\sim \vert \phi\vert^n$ where $0<n<1$ and in the presence of a perfect fluid, both numerically and analytically, using a proper generalized expansion ansatz for the scale factor and the scalar field close to the singularity. This generalized ansatz includes linear and quadratic terms, which dominate close to the singularity and cannot be ignored when estimating the Hubble parameter and the scalar field energy density; as a result, they are important for analysing the observational signatures of such singularities. We derive analytical expressions for the power (strength) of the singularity in terms of the power $n$ of the scalar field potential. We then extend the analysis to the case of scalar tensor quintessence models with the same scalar field potential in the presence of a perfect fluid, and show that a Sudden Future Singularity (SFS) occurs in this case. We derive both analytically and numerically the strength of the singularity in terms of the power $n$ of the scalar field potential.