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 _ { 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 } ) = ( -0.73 , 1.5 ) whereas the transition redshift is z _ { t } = 0.49 ^ { +0.14 } _ { -0.07 } ( 1 \sigma ) ^ { +0.54 } _ { -0.12 } ( 2 \sigma ) .
This kinematic result is in agreement with some independent analyzes and accommodates more easily many dynamical flat models ( like \Lambda CDM ) .