Updated constraints on f(R) gravity from cosmography

We address the issue of constraining the class of f(R) gravity able to reproduce the observed cosmological acceleration, by using the so-called cosmography of the Universe. We consider a model independent procedure to build up a f(z) series in terms of the measurable cosmographic coefficients; we therefore derive cosmological late time bounds on f(z) and its derivatives up to the fourth order, by fitting the luminosity distance directly in terms of such coefficients. We perform a Monte Carlo analysis, by using three different statistical sets of cosmographic coefficients, in which the only assumptions are the validity of the cosmological principle and that the class of f(R) gravity reduces to \LambdaCDM when 𝑧≪1. We use the updated union 2.1 for supernovae Ia, the constraint on the 𝐻0 value imposed by the measurements of the Hubble space telescope and the Hubble data set, with measures of 𝐻 at different 𝑧. We find a statistically good agreement of the f(R) class under examination with the cosmological data; we thus propose a candidate for f(R) gravity, which is able to pass our cosmological test, reproducing the late time acceleration in agreement with observations.