Constraints on Kinematic Model from Recent Cosmic Observations: SN Ia, BAO and Observational Hubble Data

Abstract

In this paper, linear first order expansion of deceleration parameter $q(z)=q_0+q_1(1-a)$ ($M_1$), constant jerk $j=j_0$ ($M_2$) and third order expansion of luminosity distance ($M_3$) are confronted with cosmic observations: SCP 307 SN Ia, BAO and observational Hubble data (OHD). Likelihood is implemented to find the best fit model parameters. All these models give the same prediction of the evolution of the universe which is undergoing accelerated expansion currently and experiences a transition from decelerated expansion to accelerated expansion. But, the transition redshift depends on the concrete parameterized form of the model assumed. $M_1$ and $M_2$ give value of transition redshift about $z_t\sim 0.6$. $M_3$ gives a larger one, say $z_t\sim 1$. The $\chi^2/dof$ implies almost the same goodness of the models. But, for its badness of evolution of deceleration parameter at high redshift $z>1$, $M_3$ can not be reliable. $M_1$ and $M_2$ are compatible with $\Lambda$CDM model at the $2\sigma$ and $1\sigma$ confidence levels respectively. $M_3$ is not compatible with $\Lambda$CDM model at $2\sigma$ confidence level. From $M_1$ and $M_2$ models, one can conclude that the cosmic data favor a cosmological model having $j_0<-1$.