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Accelerating universe in higher dimensional space time: an alternative approach

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Abstract

We have discussed here a higher dimensional cosmological model and explained the recent acceleration with a Chaplygin type of gas. Dimensional reduction of extra space is possible in this case. Our solutions are general in nature because all the well known results of 4D Chaplygin driven cosmology are recovered when \(d = 0\). We have drawn the best fit graph using the data obtained by the differential age method and it is seen that the graph favours only one extra dimension. That means the Chaplygin gas is apparently dominated by a 5D world. Relevant to point out that the final equation in this case are highly nonlinear in nature. Naturally it is not possible to obtain explicit solution of the 4D scale factor with time. To circumvent this difficulty, we consider a first order approximation of the key equation which has made it possible to get time explicit solution of 4D scale factor in exact form as well as the expression of extra dimensions. It may be pointed out that for large four dimensional scale factor this solution mimics \(\Lambda \)CDM model. An analysis of flip time is also studied both analytically and graphically in some detail. It clearly shows that early flip occurs for higher dimensions. It is also seen that the rate of dimensional reduction is faster for higher dimensions. So we may conclude that the effect of compactification of extra dimension helps the acceleration.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: There are no associated data available.]

Notes

  1. By rescaling of time parameter the Eq. (33) may also be written as \(w(t) = -\frac{2M}{k} tanh^2 \omega (t-t_0)\), when \(t = t_0\), \(w(t) =0\), i.e., \(p = 0\) implying dust dominated universe

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Acknowledgements

DP acknowledges financial support of Sree Chaitanya College, Habra for a Minor Research project vide no SCC/MRP/2019-20/03.

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Authors and Affiliations

  1. Sree Chaitanya College, Habra, 743268, India

    D. Panigrahi

  2. Relativity and Cosmology Research Centre, Jadavpur University, Kolkata, 700032, India

    D. Panigrahi & S. Chatterjee

  3. Department of Physics, University of North Bengal, Darjeeling, 734013, India

    B. C. Paul

  4. New Alipore College (retd.), Kolkata, 700053, India

    S. Chatterjee

Authors
  1. D. Panigrahi
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Correspondence to D. Panigrahi.

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Panigrahi, D., Paul, B.C. & Chatterjee, S. Accelerating universe in higher dimensional space time: an alternative approach. Eur. Phys. J. Plus 136, 771 (2021). https://doi.org/10.1140/epjp/s13360-021-01754-9

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