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In the last dozen years a wide and variegated mass of observational datarevealed that the universe is now expanding at an accelerated rate. In theabsence of a well-based theory to interpret the observations, cosmographyprovides information about the evolution of the Universe from measureddistances, only assuming that the geometry of the can be described by theFriedmann-Lemaitre-Robertson -Walker metric. We perform a high-redshiftanalysis allows us to put constraints on the cosmographic parameters up to the5fth order, thus inducing indirect constraints on any gravity theory. Here weare interested in the so called teleparallel gravity theory, f(T). Actually weuse the analytical expressions of the present day values of f(T) and itsderivatives as functions of the cosmographic parameters to map the cosmographyregion of confidences into confidence ranges for f(T) and its derivative.Moreover, we show how these can be used to test some teleparallel gravitymodels without solving the dynamical equations. Our analysis is based on theUnion2 Type Ia Supernovae (SNIa) data set, a set of 28 measurements of theHubble parameter, the Hubble diagram constructed from some Gamma Ray Bursts(GRB) luminosity distance indicators, and gaussian priors on the distance fromthe Baryon Acoustic Oscillations (BAO), and the Hubble constant h. To performour statistical analysis and to explore the probability distributions of thecosmographic parameters we use the Markov Chain Monte Carlo Method (MCMC).

Updated F(T) gravity constraints from high redshift cosmography