Finite-time future singularities models in $f(T)$ gravity and the effects of viscosity

TL;DR

This paper explores models of future finite-time singularities within $f(T)$ gravity, analyzing the impact of different viscous fluid cases on the occurrence or avoidance of singularities.

Contribution

It introduces specific $f(T)$ models for various singularity types and examines how viscosity influences their development or prevention.

Findings

Viscosity can prevent Big Rip and Big Freeze singularities for certain parameters.

Different viscosity models have distinct effects on the robustness of singularities.

The study provides new $f(T)$ models tailored to singularity types.

Abstract

We investigate models of future finite-time singularities in $f(T)$ theory, where $T$ is the torsion scalar. The algebraic function $f(T)$ is put as the teleparallel term $T$ plus an arbitrary function $g(T)$. A suitable expression of the Hubble parameter is assumed and constraints are imposed in order to provide an expanding universe. Two parameters $\beta$ and $H_s$ that appear in the Hubble parameter are relevant in specifying the types of singularities. Differential equations of $g(T)$ are established and solved, leading to the algebraic $f(T)$ models for each type of future finite time singularity. Moreover, we take into account the viscosity in the fluid and discuss three interesting cases: constant viscosity, viscosity proportional to $\sqrt{-T}$ and the general one where the viscosity is proportional to $(-T)^{n/2}$, where $n$ is a natural number. We see that for the first and second cases, in general, the singularities are robust against the viscous fluid, while for the general case, the Big Rip and the Big Freeze can be avoided from the effects of the viscosity for some values of $n$.