Abstract
In this work, we have considered the flat FRW model of the universe in (n+2)-dimensions filled with the dark matter and the magnetic field. We present the Hubble parameter in terms of the observable parameters Ω m0 and H 0 with the redshift z and the other parameters like B 0, ω, μ 0, δ, n, w m . The natures of magnetic field B, deceleration parameter q and \(\operatorname{Om}\) diagnostic have also been analyzed for accelerating expansion of the universe. 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 (B 0,ω) and to draw the statistical confidence contour, we fixed four parameters μ 0, δ, n, w m . 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 (B 0,ω) by fixing other parameters μ 0, δ, n, w m for 4D, 5D and 6D. The best fit of distance modulus for our theoretical model and the Supernova Type Ia Union2 sample are drawn for different dimensions.
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Acknowledgements
The authors are thankful to IUCAA, Pune, India for warm hospitality where part of the work was carried out. Also UD is thankful to CSIR, Govt. of India for providing research project grant (No. 03(1206)/12/EMR-II).
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Ranjit, C., Chakraborty, S. & Debnath, U. Observational study of higher dimensional magnetic universe in non-linear electrodynamics. Astrophys Space Sci 346, 291–299 (2013). https://doi.org/10.1007/s10509-013-1441-2
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DOI: https://doi.org/10.1007/s10509-013-1441-2