Reconstruction and constraining of the jerk parameter from OHD and SNe Ia observations

Compared with the plentiful researches of the Hubble parameter and deceleration factor, the third time derivative of the scale factor $a(t)$ in the FRW cosmology, namely, the jerk parameter $j$ still lacks attention. In order to study the properties of $j$, we propose several kinds of parameterizations of $j(z)$ as a function of the redshift $z$. By setting the standard $\Lambda$CDM model as the fiducial model, we constrain the jerk models with the observational Hubble parameter data (OHD) and Type Ia Supernovae (SNe) observations. We find that the perturbation of $j(z)$ favors a value of nearly zero and the $\Lambda$CDM is well accommodated by the jerk reconstruction. We also compare the powers of OHD and SNe in constraining the jerk models in detail, and find that the newly released OHD measurement at $z=2.3$ can improve the constraint significantly, even tighter than the SNe one. Furthermore, we analyze the jerk models by calculating the Hubble parameter, equation of state, the deceleration factor and $Om(z)$ diagnostic. Our results show that the universe is indeed undergoing an accelerated expansion phase following the matter-dominated one, which is consistent with the standard model by observations.