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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 theteleparallel term $T$ plus an arbitrary function $g(T)$. A suitable expressionof the Hubble parameter is assumed and constraints are imposed in order toprovide an expanding universe. Two parameters $\beta$ and $H_s$ that appear inthe Hubble parameter are relevant in specifying the types of singularities.Differential equations of $g(T)$ are established and solved, leading to thealgebraic $f(T)$ models for each type of future finite time singularity.Moreover, we take into account the viscosity in the fluid and discuss threeinteresting 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, ingeneral, the singularities are robust against the viscous fluid, while for thegeneral case, the Big Rip and the Big Freeze can be avoided from the effects ofthe viscosity for some values of $n$.

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