Transition redshift: new constraints from parametric and nonparametric methods

Abstract

In this paper, we use the Cosmokinematics approach to study the accelerated\nexpansion of the Universe. This is a model independent approach and depends\nonly on the assumption that the Universe is homogeneous and isotropic and is\ndescribed by the FRW metric. We parametrize the deceleration parameter, $q(z)$,\nto constrain the transition redshift ($z_t$) at which the expansion of the\nUniverse goes from a decelerating to an accelerating phase. We use three\ndifferent parametrizations of $q(z)$ namely,\n$q_\\I(z)=q_{\\textnormal{\\tiny\\textsc{1}}}+q_{\\textnormal{\\tiny\\textsc{2}}}z$,\n$q_\\II (z) = q_\\3 + q_\\4 \\ln (1 + z)$ and\n$q_\\III(z)=\\frac{1}{2}+\\frac{q_{\\textnormal{\\tiny\\textsc{5}}}}{(1+z)^2}$. A\njoint analysis of the age of galaxies, strong lensing and supernovae Ia data\nindicates that the transition redshift is less than unity i.e. $z_t<1$. We also\nuse a nonparametric approach (LOESS+SIMEX) to constrain $z_t$. This too gives\n$z_t<1$ which is consistent with the value obtained by the parametric approach.\n