Transition Redshift: New constraints from parametric and nonparametric methods

Abstract: 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, $q_\I(z)=q_{\textnormal{\tiny\textsc{1}}}+q_{\textnormal{\tiny\textsc{2}}}z$, $q_\II (z) = q_\3 + q_\4 \ln (1 + z)$ and $q_\III(z)=\frac{1}{2}+\frac{q_{\textnormal{\tiny\textsc{5}}}}{(1+z)^2}$. 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.