f(T) cosmology against the cosmographic method: A new study using mock and observational data

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In this paper, we study the power-law $f(T)$ model using Hubble diagrams of type Ia supernovae (SNIa), quasars (QSOs), Gamma Ray Bursts (GRBs) and the measurements from baryonic acoustic oscillations (BAO) in the framework of the cosmographic method.

• Using mock data for SNIa, QSOs and GRBs generated based on the power-law $f(T)$ model, we show whether different cosmographic methods are suitable to reconstruct the distance modulus or not.
• In particular, we investigate the rational PADE polynomials $(3,2)$ and $(2,2)$ in addition to the fourth- and fifth- order Taylor series.
• We show that PADE $(3,2)$ is the best approximation that can be used in the cosmographic method to reconstruct the distance modulus at both low and high redshifts.