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) = q1 + q2/1 +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 zT and current deceleration parameter q0 are given as zT = 0.65-0.12 +0.25 and q0 = 0.76 -0.15+0.15(1σ). Furthermore, in the 5D bounce model it can be seen that the evolution of equation of state (EOS) for dark energy wde can cross over -1 at about z = 0.23 and the current value w0de =-1.15 <-1. On the other hand, by giving a concrete expression of model-independent EOS of dark energy wde, in the 5D bounce model we obtain the best fitting values zT = 0.66 -0.08+0.11 and q0 = 0.69-0.10+ 0.10(1σ) 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.
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