Infinite-time singularities models and possible avoidance

Abstract

In this work, we explore two models of future Infinite time singularities in f(T) theory, where T is the torsion scalar. We consider the algebraic function g(T) as the teleparallel term T plus arbitrary function f(T). A suitable Hubble parameter expression is assumed to characterize both of the two singularities models and an expanding universe is provided from imposed constraints. We solve differential equations of g(T) and obtain the algebraic g(T) models of each type of future infinite singularity. In order to study the possible avoidance of singularities, we take into account the viscosity in the fluid and explore three interesting cases: constant viscosity δo, non-constant viscosity proportional to energy density δoρα with α a real parameter and the general case where the viscosity is proportional to (−T)n2, where n is a natural number. We notice that in the first case, the Little Rip singularity may be avoided but the Pseudo Rip is robust against the viscous fluid while for the non-constant viscosity and general case, both singularities cannot be avoided.