Transition redshift from the V-reconstruction method

We show the effectiveness of using the procedure of the potential reconstruction (the V-method) in the estimation of the transition redshift corresponding to switch from deceleration to acceleration phase of the Universe. We investigate the FRW models with dark energy by applying the particle-like description of their dynamics. In this picture the evolution of the universe is represented by motion of a fictitious particle in the one-dimensional potential $V(a)$ or V(z)$where$a$is the scale factor and$z$is the redshift. The V-method solves the inverse problem where we reconstruct the potential function from empirical data. We use the Riess et al.'s gold and gold+silver samples of SN Ia data in this reconstruction. In the same framework we obtain both the estimates of the form of the equation of state for dark energy and the transition redshift. We obtain that transition redshift is$0.38_{-0.07}^{+0.10}$(gold subset) and$0.37_{-0.07}^{+0.06}$(gold+silver sample) when the linear model of dark energy ($w(z)=w_{0} + w_{1}z$) and$\Omega_{m,0}=0.3$ are assumed. We compare the estimation of transition redshift with the Riess et al. results. The V-method also alows us to find the value of Hubble function at the moment of transition.