Isotropic inhomogeneous cosmological model with torsion

An isotropic, inhomogeneous cosmology with torsion and cosmological constant is considered in the context of the Lemaitre-Tolman-Bondi metric. The form of the torsion tensor isdetermined from the isotropy of space. The field equations are derived by varying the Einstein-Cartan-Hilbert action with respect to the metric tensor and considering the torsion as a parameter. Consistency of the field equation implies that only the axial part of the torsion is of relevance and that torsion differs from pression by an arbitrary time dependent function. If such function is taken constant, the scheme admits inflationary phases, but torsion is irrelevant because it amounts to a re-definition of the cosmological constant. On the contrary, if that function is not constant, the scheme is much more difficult to be integrate, but torsion results to be an effective suitable parameter to fit observational data.