Constraints on the transition redshift using Hubble phase space portrait

Abstract

One of the most significant discoveries in modern cosmology is that the universe is currently in a phase of accelerated expansion after a switch from a decelerated expansion. The redshift corresponding to this epoch is commonly referred to as the transition redshift [Formula: see text]. In this work, we put constraints on the transition redshift with both model-independent and model-dependent approaches. We consider the recently compiled database of 32 Hubble parameter measurements and the Pantheon sample of Type Ia Supernovae (SNe). In order to include the possible systematic effects in this analysis, we use the full covariance matrix of systematic uncertainties for the Hubble parameter measurements. We plot a Hubble Phase Space Portrait (HPSP) between [Formula: see text] and [Formula: see text] in a model-independent way. From this HPSP diagram, we estimate the transition redshift as well as the current value of the equation of state parameter [Formula: see text] in a model-independent way. By considering H(z) measurements, we find the best fit value of [Formula: see text] and [Formula: see text]. We obtain the best fit value of [Formula: see text] and [Formula: see text] using the Pantheon database. Further, we also use a model-dependent approach to determine [Formula: see text]. Here, we consider a nonflat [Formula: see text]CDM model as a background cosmological model. We reconstruct the cosmic triangle plot among [Formula: see text], [Formula: see text] and [Formula: see text] where the constraints of each parameter are determined by the location in this triangle plot. By using [Formula: see text] and [Formula: see text] values, we find the best value of the transition redshift [Formula: see text], which is in good agreement with the Planck 2018 results at [Formula: see text] confidence level. We also simulate the observed Hubble parameter measurements in the redshift range [Formula: see text] and perform the same analysis to estimate the transition redshift.