Transition redshift: new constraints from parametric and nonparametric methods

In this paper, we use the cosmokinematics approach to study the accelerated expansion of the Universe. This is a model independent approach and depends only on the assumption that the Universe is homogeneous and isotropic and is described by the FRW metric. We parametrize the deceleration parameter, q(z), to constrain the transition redshift (z_t) at which the expansion of the Universe goes from a decelerating to an accelerating phase. We use three different parametrizations of q(z) namely, q_I(z)=q₁+q₂z, q_II (z) = q₃ + q₄  ln  (1 + z) and q_III (z)=½+q₅/(1+z)². A joint analysis of the age of galaxies, strong lensing and supernovae Ia data indicates that the transition redshift is less than unity i.e. z_t < 1. We also use a nonparametric approach (LOESS+SIMEX) to constrain z_t. This too gives z_t < 1 which is consistent with the value obtained by the parametric approach.