Phenomenological Reconstruction of $f(T)$ Teleparallel Gravity
  We present a novel reconstruction method of $f(T)$ teleparallel gravity from
phenomenological parameterizations of the deceleration parameter or other
alternatives. This can be used as a toolkit to produce viable modified gravity
scenarios directly related to cosmological observations. We test two
parameterizations of the deceleration parameter considered in recent
literatures in addition to one parametrization of the effective (total)
equation of state (EoS) of the universe. We use the asymptotic behaviour of the
matter density parameter as an extra constraint to identify the viable range of
the model parameters. One of the tested models shows how tiny modification can
produce viable cosmic scenarios quantitatively similar to $\Lambda$CDM but
qualitatively different whereas the dark energy (DE) sector becomes dynamical
and fully explained by modified gravity not by a cosmological constant.
