content_image/359053.jpg content_image/359052.jpg content_image/359051.jpg content_image/359050.jpg content_image/359049.jpg content_image/359048.jpg content_image/359047.jpg
and effective distance are 

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The redshift z$_{d}$ at the baryon drag epoch is fitted with the formula [19] 

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where Ω$_{m}$$_{0}$ is the current value of the dimensionless matter energy density, Ω$_{b}$ is the di- mensionless baryon matter energy density, and h = H$_{0}$/ 100. The sound speed c$_{s}$ ( z ) = 1 / √ 3[1 + ¯ R$_{b}$/ (1 + z )], where ¯ R$_{b}$ = 315000Ω$_{b}$ h $^{2}$( T$_{cmb}$/ 2 . 7K) − 4 and T$_{cmb}$ = 2 . 726K. In [8], two points d$_{0}$$_{.}$$_{2}$ and d$_{0}$$_{.}$$_{35}$ and their covariance matrix are given. We will use d$_{0}$$_{.}$$_{2}$ = 0 . 1905 ± 0 . 0061, d$_{0}$$_{.}$$_{35}$ = 0 . 1097 ± 0 . 0036 and their covariance matrix (hereafter Bao2) as the second sample of BAO data in the data fitting. When we use these data, we add two more parameters Ω$_{b}$ h 2 and h . Based on these two BAO distance measurements, we can derive the BAO distance ratio D$_{V}$ (0 . 35) /D$_{V}$ (0 . 2) = 1 . 736 ± 0 . 065 (hereafter BaoR), which is relatively model inde- pendent quantity. This BAO distance ratio was employed in the analysis in [11]. In our case we will further use another two radial BAO data at redshifts z = 0 . 24 and z = 0 . 43 [20] by using Δ z ( z ) = H ( z ) r$_{s}$ ( z$_{d}$ ) /c (hereafter BaoZ). Combining BAO data sets Bao2 and BaoZ, we have the data set called Bao4. Therefore, for different BAO data sets, we can perform χ 2 statistics for the model parameter p as follows 

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and 

where i, j = 0 . 2 , 0 . 35, Δ d$_{0}$$_{.}$$_{2}$ = d$_{0}$$_{.}$$_{2}$ − 0 . 1905, Δ d$_{0}$$_{.}$$_{35}$ = d$_{0}$$_{.}$$_{35}$ − 0 . 1097. 

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Since the SNIa and BAO data contain information about the universe at relatively low redshifts, we will include the CMB information by implementing the Wilkinson microwave anisotropy probe 5 year (WMAP5) data to probe the entire expansion history up to the last 

