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

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.

To be published in Chinese Physics C (Accepted version)

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Cited by in corpus (11)

• Teleparallel Gravity: From Theory to Cosmology
• Cosmological bouncing solutions in f(T,B) gravity
• Constant-roll Inflation in $f(T)$ Teleparallel Gravity
• Dynamical systems approach and generic properties of $f(T)$ cosmology
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• $H_0$ Tension and the Phantom Regime: A Case Study In Terms of an Infrared $f(T)$ Gravity
• Rotating and non-rotating AdS black holes in $f(\mathcal{T})$ gravity non-linear electrodynamics
• A preference for dynamical phantom dark energy using one-parameter model with Planck, DESI DR1 BAO and SN data
• $f(T)$ cosmology: From Pseudo-Bang to Pseudo-Rip
• Constraints on the Transition Redshift using Hubble Phase Space Portrait
• Effect of nonlocal transformations on the linearizability and exact solvability of the nonlinear generalized modified Emden type equations