We study weak-field solutions having spherical symmetry in f (T ) gravity; to this end, we solve the field equations for a non diagonal tetrad, starting from Lagrangian in the form f (T ) = T +αT n , where α is a small constant, parameterizing the departure of the theory from GR. We show that the classical spherically symmetric solutions of GR, i.e. the Schwarzschild and Schwarzschild-de Sitter solutions, are perturbed by terms in the form ∝ r 2−2n and discuss the impact of these perturbations in observational tests. * Electronic address: matteo.ruggiero@polito.it † Electronic address: ninfa.radicella@sa.infn.it

It is argued that the discovery of cosmic acceleration could have been anticipated on thermodynamic grounds, namely, the generalized second law and the approach to equilibrium at large scale factor. Therefore, the existence of dark energy -or equivalently, some modified gravity theoryshould have been expected. In general, cosmological models that satisfy the above criteria show compatibility with observational data.a

We apply the generalized second law of thermodynamics to discriminate among quantum corrections (whether logarithmic or power-law) to the entropy of the apparent horizon in spatially Friedmann-Robertson-Walker universes. We use the corresponding modified Friedmann equations along with either Clausius relation or the principle of equipartition of the energy to set limits on the value of a characteristic parameter entering the said corrections.PACS numbers: 98.80.Jk, 95.30.Tg.