Kinematic Constraints to the Transition Redshift from SNe Ia Union Data

Abstract

The kinematic approach to cosmological tests provides a direct evidence to the present accelerating stage of the universe which 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, $q(z)=q_0+q_1z$, 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 ($q_0,q_1$) = ($-0.73,1.5)$ whereas the transition redshift is $z_t = 0.49^{+0.14}_{-0.07}$ ($1σ$) $^{+0.54}_{-0.12}$ ($2σ$). This kinematic result is in agreement with some independent analyzes and accommodates more easily many dynamical flat models (like $Λ$CDM).