Bianchi type i in f(T) gravitational theories

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© 2016 Chinese Physical Society and IOP Publishing Ltd. A tetrad field that is homogeneous and anisotropic which contains two unknown functions A(t) and B(t) of cosmic time is applied to the field equations of f (T), where T is the torsion scalar, T = TμνρSμνρ. We calculate the equation of continuity and rewrite it as a product of two brackets, the first is a function of f (T) and the second is a function of the two unknowns A(t) and B(t). We use two different relations between the two unknown functions A(t) and B(t) in the second bracket to solve it. Both of these relations give constant scalar torsion and solutions coincide with the de Sitter one. So, another assumption related to the contents of the matter fields is postulated. This assumption enables us to drive a solution with a non-constant value of the scalar torsion and a form of f (T) which represents ΛCDM.

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