Cosmographic transition redshift in $f(R)$ gravity

We propose a strategy to infer the transition redshift $z_{da}$, which characterizes the passage through the universe decelerated to accelerated phases, in the framework $f(R)$ gravities. To this end, we numerically reconstruct $f(z)$, i.e. the corresponding $f(R)$ function re-expressed in terms of the redshift $z$ and we show how to match $f(z)$ with cosmography. In particular, we relate $f(z)$ and its derivatives to the cosmographic coefficients, i.e. $H_0, q_0$ and $j_0$ and demonstrate that its corresponding evolution may be framed by means of an effective logarithmic dark energy term $\Omega_X$, slightly departing from the case of a pure cosmological constant. Afterwards, we show that our model predicts viable transition redshift constraints, which agree with $\Lambda$CDM. To do so, we compute the corresponding $z_{da}$ in terms of cosmographic outcomes and find that $z_{da}\leq1$. Finally, we reproduce an effective $f(z)$ and show that this class of models is fairly well compatible with present-time data. To do so, we get numerical constraints employing Monte Carlo fits with the Union 2.1 supernova survey and with the Hubble measurement data set.