Cosmography in<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

Based only on the assumption that the Universe is homogenous and isotropic on large scales, cosmography is an ideal tool to investigate the cosmic expansion history in an almost model-independent way. Fitting the data on the luminosity distance and baryon acoustic oscillations allows to determine the confidence ranges for the cosmographic parameters hence giving some quantitative constraints that at whatever theory has to fulfill. As an application, we consider here the case of teleparallel gravity also referred to as $f(T)$ gravity. To this end, we first work out analytical expressions to express the present day values of $f(T)$ derivatives as a function of the cosmographic parameters, which hold under quite general and physically motivated conditions. We then use the constraints coming from cosmography to find out the confidence ranges for $f(T)$ derivatives up to the fifth order and show how these can be used to check the viability of given teleparallel gravity models without the need to explicitly solve the second order dynamic equations.

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