Model independent constraints on transition redshift

TLDR: In this article, a cosmological-model independent framework for the transition redshift was proposed, which determines the onset of cosmic acceleration, in a flat universe and is based on a parametrization for the comoving distance.

Abstract: This paper aims to put constraints on the transition redshift $z_t$, which determines the onset of cosmic acceleration, in cosmological-model independent frameworks. In order to perform our analyses, we consider a flat universe and {assume} a parametrization for the comoving distance $D_C(z)$ up to third degree on $z$, a second degree parametrization for the Hubble parameter $H(z)$ and a linear parametrization for the deceleration parameter $q(z)$. For each case, we show that {type Ia supernovae} and $H(z)$ data complement each other on the parameter {space} and tighter constrains for the transition redshift are obtained. By {combining} the type Ia supernovae observations and Hubble parameter measurements it is possible to constrain the values of $z_t$, for each approach, as $0.806\pm 0.094$, $0.870\pm 0.063$ and $0.973\pm 0.058$ at 1$\sigma$ c.l., respectively. Then, such approaches provide cosmological-model independent estimates for this parameter.