A kinematic method to probe cosmic acceleration

We propose a method to map the cosmological evolution of the main kinematic parameters H, q and j from observational data. Unlike the traditional approach, the methodology here discussed provides constraints on the kinematic parameters not only at z=0 but also at any value of the redshift parameter. By choosing the scale factor as expansion variable in order to avoid the series convergence and truncation problems, we perform a Taylor expansion of the luminosity distance around an arbitrary a˜ and use current type Ia supernovae data to estimate the values of H, q and j for 0.41≲a˜⩽1 (0⩽z⩽1.4). We show that the transition from a decelerated phase to an accelerating one occurs in the range 0.4≲z≲0.9 and that for z≳0.5 the value of j=1 is ruled out in 2σ confidence level.