Model independent reconstruction of cosmological accelerated-decelerated phase

We propose two model independent methods to obtain constraints on the transition and equivalence redshifts zₜᵣ, zeq. In particular, we consider zₜᵣ as the onset of cosmic acceleration, whereas zeq 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 zeq is not allowed to span. To this end, we discuss how to build up cosmographic expansions in terms of zₜᵣ 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 1σ confidence level the ΛCDM predictions on zₜᵣ and zeq are slightly confirmed, although at 2σ confidence level dark energy expectations cannot be excluded. Finally, we theoretically interpret our outcomes and discuss possible limitations of our overall approach.