Energy conditions bounds on f(T) gravity
  In standard approach to cosmological modeling in the framework of general
relativity, the energy conditions play an important role in the understanding
of several properties of the Universe, including singularity theorems, the
current accelerating expansion phase, and the possible existence of the
so-called phantom fields. Recently, the $f(T)$ gravity has been invoked as an
alternative approach for explaining the observed acceleration expansion of the
Universe. If gravity is described by a $f(T)$ theory instead of general
relativity, there are a number of issues that ought to be reexamined in the
framework of $f(T)$ theories. In this work, to proceed further with the current
investigation of the limits and potentialities of the $f(T)$ gravity theories,
we derive and discuss the bounds imposed by the energy conditions on a general
$f(T)$ functional form. The null and strong energy conditions in the framework
of $f(T)$ gravity are derived from first principles, namely the purely
geometric Raychaudhuri's equation along with the requirement that gravity is
attractive. The weak and dominant energy conditions are then obtained in a
direct approach via an effective energy-momentum tensor for $f(T)$ gravity.
Although similar, the energy condition inequalities are different from those of
general relativity (GR), but in the limit $f(T)=T$ the standard forms for the
energy conditions in GR are recovered. As a concrete application of the derived
energy conditions to locally homogeneous and isotropic $f(T)$ cosmology, we use
the recent estimated value of the Hubble parameter to set bounds from the weak
energy condition on the parameters of two specific families of $f(T)$ gravity
theories.
