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Observational Constraints of Homogeneous Higher Dimensional Cosmology with Modified Chaplygin Gas

In this work, we have considered the flat FRW model of the universe in $(n+2)$-dimensions filled with the dark matter (perfect fluid with negligible pressure) and the modified Chaplygin gas (MCG) type dark energy. We present the Hubble parameter in terms of the observable parameters $Ω_{m0}$, $Ω_{x0}$ and $H_{0}$ with the redshift $z$ and the other parameters like $A$, $B$, $C$, $n$ and $α$. From Stern data set (12 points), we have obtained the bounds of the arbitrary parameters by minimizing the $χ^{2}$ test. The best-fit values of the parameters are obtained by 66%, 90% and 99% confidence levels. Now to find the bounds of the parameters and to draw the statistical confidence contour, we first fixed three parameters $C, n, α$ and then fixed the three parameters $A, n, α$. In the first case we find the bounds of $(A, B)$ and draw the contour between them for 4D$(n=2)$, 5D$(n=3)$ and 6D$(n=4)$. In the second case we fixed three different values of A as 1, 1/3, -1/3 to find the bounds of $(B, C)$ and draw the contour between them. Here the parameter $n$ determines the higher dimensions and we perform comparative study between three cases : 4D $(n=2)$, 5D $(n=3)$ and 6D $(n=4)$ respectively. Next due to joint analysis with BAO observation, we have also obtained the bounds of the parameters ($A,B$) by fixing some other parameters $α$ and $A$ for 4D, 5D and 6D.