Observational constraints on the accelerating universe in the framework of a 5D bounce cosmological model

In the framework of a five-dimensional (5D) bounce cosmological model, a useful function $f(z)$ is obtained by giving a concrete expression of deceleration parameter $q(z)=q_1+\dfrac{q_2}{1+\ln (1+ z)}$. Then using the obtained Hubble parameter $H(z)$ according to the function $f(z)$, we constrain the accelerating universe from recent cosmic observations: the 192 ESSENCE SNe Ia and the 9 observational $H(z)$ data. The best fitting values of transition redshift $z_T$ and current deceleration parameter $q_0 $ are given as $z_T = 0.65_{ - 0.12}^{ + 0.25} $ and $q_0 = - 0.76_{ - 0.15}^{ + 0.15} (1\sigma )$. Furthermore, in the 5D bounce model it can be seen that the evolution of equation of state (EOS) for dark energy $w_{\rm de} $ can cross over $-1$ at about $z=0.23$ and the current value $w_{\rm 0de} = - 1.15<- 1$. On the other hand, by giving a concrete expression of model-independent EOS of dark energy $w_{\rm de} $, in the 5D bounce model we obtain the best fitting values $z_T = 0.66_{ - 0.08}^{ + 0.11} $ and $q_0 = - 0.69_{ - 0.10}^{ + 0.10} (1\sigma)$ from the recently observed data: the 192 ESSENCE SNe Ia, the observational $H(z)$ data, the 3-year Wilkinson Microwave Anisotropy Probe (WMAP), the Sloan Digital Sky Survey (SDSS) baryon acoustic peak and the x-ray gas mass fraction in clusters.