# Generic Phase Portrait Analysis of the Finite-time Singularities and Generalized Teleparallel Gravity

## TL;DR

This paper uses phase portrait analysis to classify finite-time singularities in cosmology, applies it to f(T) gravity, and explores the role of torsion fluid in singularity formation.

## Contribution

It introduces a generic phase portrait framework for finite-time singularities and reconstructs f(T) gravity models consistent with this approach.

## Key findings

- Classified four types of finite-time singularities using phase portraits.
- Reconstructed f(T) gravity models that produce these singularities.
- Highlighted the significance of torsion fluid in cosmological singularities.

## Abstract

We analyze the common four types of the finite-time singularities using a generic framework of the phase portrait geometric approach. This technique requires that the Friedmann system to be written as a one dimensional autonomous system. We employ a scale factor that has been used widely in literature to realize the four finite-time singularity types, then we show a detailed discussion for each case showing possible novel models. Moreover, we show how different singularity types can play essential roles in different cosmological scenarios. Among several modified gravity theories, we show that the f (T) cosmology is in comfort with the phase portrait analysis, since the field equations include Hubble derivatives only up to first order. Therefore, we reconstruct the f (T) theory which generates these phase portraits. We also perform a complementary analysis using the effective equation of state. Furthermore, we investigate the role of the torsion fluid in realizing the cosmic singularities.