Unimodular f(T) gravity

Abstract.We have set the goal to reconstruct the geometric actions f(T) in unimodular f (T) gravity. The unimodular f (T) gravity gave us stunning properties related to the way we write the modified Friedmann equations. Indeed, it has been found that depending on how the Friedmann equations are given, the Lagrange multipliers may or not depend on the time parameter $\tau$τ, and at the same time the reconstruction functions f(T) can easily be made generallly (not depending on the given scale factor) or determine a particular way (depending on the given scale factor), in the vacuum. It is noted that the reconstruction of a general action joins a philosophy of unimodular gravity for the constant $\lambda$λ.