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 and z_eq, respectively. 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 by 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 catalogues. We show that at 1σ confidence level the Lambda cold dark matter predictions on z_tr and z_eq 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.