Model independent reconstruction of cosmological accelerated-decelerated
  phase
  We propose two model independent methods to obtain constraints on the
transition and equivalence redshifts $z_{tr}$, $z_{eq}$. In particular, we
consider $z_{tr}$ as the onset of cosmic acceleration, whereas $z_{eq}$ the
redshift at which the densities of dark energy and pressureless matter are
equated. With this prescription, we expand the Hubble and deceleration
parameters up to two hierarchical orders and show a linear correlation between
transition and equivalence, from which we propose exclusion plots where
$z_{eq}$ is not allowed to span. To this end, we discuss how to build up
cosmographic expansions in terms of $z_{tr}$ and compute the corresponding
observable quantities directly fitting the luminosity and angular distances and
the Hubble rate with cosmic data. We make our computations through Monte Carlo
fits involving type Ia supernova, baryonic acoustic oscillation and Hubble most
recent data catalogs. We show at $1\sigma$ confidence level the $\Lambda$CDM
predictions on $z_{tr}$ and $z_{eq}$ are slightly confirmed, although at
$2\sigma$ confidence level dark energy expectations cannot be excluded.
Finally, we theoretically interpret our outcomes and discuss possible
limitations of our overall approach.
