Kinematic constraints to the transition redshift from supernovae type Ia union data

Abstract

The kinematic approach to cosmological tests provides direct evidence to the present accelerating stage of the Universe that does not depend on the validity of general relativity, as well as on the matter-energy content of the Universe. In this context, we consider here a linear two-parameter expansion for the decelerating parameter, $q(z)={q}_{0}+{q}_{1}z$, where ${q}_{0}$ and ${q}_{1}$ are arbitrary constants to be constrained by the union supernovae data. By assuming a flat Universe we find that the best fit to the pair of free parameters is $({q}_{0},{q}_{1})=(\ensuremath{-}0.73,1.5)$ whereas the transition redshift is ${z}_{t}={0.49}_{\ensuremath{-}0.07}^{+0.14}(1\ensuremath{\sigma})$ $\genfrac{}{}{0}{}{+0.54}{\ensuremath{-}0.12}(2\ensuremath{\sigma})$. This kinematic result is in agreement with some independent analyses and more easily accommodates many dynamical flat models (like $\ensuremath{\Lambda}\mathrm{CDM}$).