Energy conditions bounds on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity

In the 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 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, but in the limit $f(T)=T$, the standard forms for the energy conditions in general relativity 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.

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