Eur. Phys. J. Plus (2013) 128: 53
https://doi.org/10.1140/epjp/i2013-13053-9

Regular Article

Observational constraints of homogeneous higher-dimensional cosmology with modified Chaplygin gas

¹³⁴⁴ Department of Mathematics, Seacom Engineering College, 711 302, Howrah, India
²³⁴⁴ Department of Mathematics, Bengal Engineering and Science University, 711 103, Howrah, India

^* e-mail: chayanranjit@gmail.com

Received: 15 January 2013
Revised: 19 April 2013
Accepted: 3 May 2013
Published online: 27 May 2013

Abstract

In this work, we have considered the flat FRW model of the universe in (n + 2) dimension filled with 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 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 dimension and we perform a comparative study between three cases: 4D (n = 2), 5D (n = 3) and 6D (n = 4), respectively. Next due to the joint analysis with the 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.