Cosmographic bounds on the cosmological deceleration-acceleration
  transition redshift in $f(\mathcal{R})$ gravity
  We examine the observational viability of a class of $f(\mathcal{R})$ gravity
cosmological models. Particular attention is devoted to constraints from the
recent observational determination of the redshift of the cosmological
deceleration-acceleration transition. Making use of the fact that the Ricci
scalar is a function of redshift $z$ in these models, $\mathcal {R=R}(z)$, and
so is $f(z)$, we use cosmography to relate a $f(z)$ test function evaluated at
higher $z$ to late-time cosmographic bounds. First, we consider a model
independent procedure to build up a numerical $f(z)$ by requiring that at $z=0$
the corresponding cosmological model reduces to standard $\Lambda$CDM. We then
infer late-time observational constraints on $f(z)$ in terms of bounds on the
Taylor expansion cosmographic coefficients. In doing so we parameterize
possible departures from the standard $\Lambda$CDM model in terms of a
two-parameter logarithmic correction. The physical meaning of the two
parameters is also discussed in terms of the post Newtonian approximation.
Second, we provide numerical estimates of the cosmographic series terms by
using Type Ia supernova apparent magnitude data and Hubble parameter
measurements. Finally, we use these estimates to bound the two parameters of
the logarithmic correction. We find that the deceleration parameter in our
model changes sign at a redshift consistent with what is observed.
