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

We investigate models of future finite-time singularities in f(T) theory, where T is the torsion scalar. The algebraic function f(T) is the teleparallel term, T, plus an arbitrary function, g(T). A suitable expression for the Hubble parameter is assumed and constraints are imposed to provide an expanding universe. Two parameters, [beta] and [H.sub.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 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 [square root of (-T)], and the general one where the viscosity is proportional to [(-T).sup.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. PACS Nos.: 95.36.+x, 04.50.Kd, 66.20.-d. Nous analysons la theorie des modeles de singularites de temps futur fini, f(T)ou T est le scalaire de torsion. La fonction algebrique est posee comme etant le terme teleparallele de T plus une fonction g(T). Nous supposons une expression adequate pour le parametre de Hubble et nous imposons des contraintes de facon a avoir un univers en expansion. Les deux parametres [beta] et [H.sub.s] qui apparaissent dans l'expression pour le parametre de Hubble sont pertinents pour specifier les types de singularite. Nous etablissons et solutionnons les equations differentielles pour g(T), menant aux modeles algebriques f(T) pour chaque type de singularite de temps futur fini. Nous tenons egalement compte de la viscosite du fluide et discutons trois cas interessants: viscosite constante, viscosite proportionnelle a [square root of (-T)] et un cas general ou la viscosite est proportionnelle a [(-T).sup.n/2], ou n est un entier naturel. Pour les deux premiers cas, generalement les singularites sont robustes devant la viscosite du fluide, alors que pour le cas general, la viscosite correspondant a certaines valeurs de n permet d'eviter la Grande Dechirure et le Grand Gel. [Traduit par la Redaction]
1. Introduction Recent observations of type Ia supernovae (SNIa) and Wilkinson microwave anisotropy probe (WMAP) [1, 2] indicate that our universe is currently undergoing an accelerating expansion, which confronts the [...]