Quantum Mechanical Explanation for Dark Energy, Cosmic Coincidence, Flatness, Age, and Size of the Universe

Biswaranjan Dikshit 1
  • 1 Laser and Plasma Technology Division, Bhabha Atomic Research Centre, Homi Bhabha National Institute, 400085, Mumbai, India


One of the most important problems in astronomy is the cosmological constant problem in which conventional calculation of vacuum energy density using quantum mechanics leads to a value which is ~10123 times more than the vacuum energy estimated from astronomical observations of expanding universe. The cosmic coincidence problem questions why matter energy density is of the same order of magnitude as the vacuum energy density at present time. Finally, the mechanism responsible for spatial flatness is not clearly understood. In this paper, by taking the vacuum as a finite and closed quantum oscillator, we solve all of the above-mentioned problems. At first, by using the purely quantum mechanical approach, we predict that the dark energy density is c4/(GR2) = 5.27×10−10 J/m3 (where R is radius of 3-sphere of the universe) and matter energy density is c4/(2GR2) = 2.6×10−10 J/m3 which match well with astronomical observations. We also prove that dark energy has always been ~66.7% and matter energy has been ~33.3% of the total energy and thus solve the cosmic coincidence problem. Next, we show how flatness of space could be maintained since the early stage of the universe. Finally, using our model, we derive the expression for age and radius of the universe which match well with the astronomical data.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • Banks, T. 2004, Physics Today, 57(3), 46-51.

  • Bars, I. & Terning, J. 2009, “Extra dimensions in Space and Time”, Springer, p. 27.

  • Berman, M. S. 1991, Phys. Rev. D, 43(4), 1075-1078.

  • Carroll, S. M. 2001, Living Rev. Relativity, 4(1), 1-56.

  • Carvalho, J. C., Lima, J. A. S., & Waga, I. 1992, Phys. Rev. D, 46(6), 2404-2407.

  • Casimir, H. B. G. 1948, Proc. Kon. Ned. Akad. Wetensch., B51, 793-795.

  • Chaboyer, B., Demarque, P., Kernan, P. J., & Krauss, L. M. 1996, Science, 271(5251), 957-961.

  • Chen, W. & Wu, Y.-S. 1990, Phys. Rev. D, 41(2), 695-698.

  • Einstein, A. 1917, “Kosmologische Betrachtungen zur allgemeinen Relativitaetstheorie” (Cosmological Considerations in the General Theory of Relativity)”, Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften Berlin, 142-152. (In German)

  • Friedmann, A. 1922, “Uber die Krummung des Raumes”, Zeitschrift fur Physik, 10, 377-386. (In German). English version – Fried-mann, A. 1999, “On the Curvature of Space”, General Relativity and Gravitation, 31(12), 1991-2000.

  • Fujii, Y. & Nishioka, T., 1990, Phys. Rev. D, 42(2), 361-370.

  • Guth, A. H. 1981, Phys. Rev. D, 23(2), 347-356.

  • Guth, A. H. 1997, Beam Line, 27(3), 14-2. (https://ned.ipac.caltech.edu/level5/Guth/Guth_contents.html).

  • Hobson, A., 2013, American Journal of Physics, 81(3), 211-223.

  • Lamoreaux, S. K. 1997, Physical Review Letters, 78(1), 5-8.

  • Lattman, E. E. 2009, European Journal of Physics, 30, L41-L42.

  • Mohideen U. and Anushree, R. 1998, Physical Review Letters, 81(21), 4549-4552.

  • Peebles, P. J. E., 2003, Reviews of Modern Physics, 75, 559-606.

  • Planck Collaboration, 2016, A&A, 594, id.A13 (63pp).

  • Rubakov, V. A. 2000, Phys. Rev. D, 61, 061501.

  • Saslow, W. M. 1998, European Journal of Physics, 19, 313.

  • Velten, H. E. S., vom Marttens, R. F., Zimdahl, W. 2014, Eur. Phys. J. C, 74, 3160.

  • Weinberg, S. 1989, Reviews of Modern Physics, 61(1), 1-23.

  • Wilson, C. M., Johansson, G., Pourkabirian, A., Simoen, M., Johansson, J. R., Duty, T. et al. 2011, Nature, 479, 376-379.

  • Yousaf, Z., Bamba, K., & Bhatti M. Z. 2016a, Phys. Rev. D, 93, 124048.

  • Yousaf, Z., Bamba, K., & Bhatti, M. Z. 2016b, Phys. Rev. D, 93, 064059.

  • Yousaf, Z. 2017, Eur. Phys. J. Plus, 132, 71.

  • Yousaf, Z. 2018, Astrophys. Space Sci., 363, 226.

  • Yousaf, Z. 2019a, Eur. Phys. J. Plus, 134, 245.

  • Yousaf, Z., Bamba, K., Bhatti, M. Z., & Ghafoor, U., 2019b, Phys. Rev. D, 100, 024062.

  • Zlatev, I., Wang, L., and Steinhardt, P. J., 1999, Physical Review Letters, 82(5), 896-899.


Journal + Issues

Open Astronomy is a peer-reviewed, fully open access online journal, that publishes research, reviews and news spanning all aspects of astronomy and astrophysics. Open Astronomy (formerly Baltic Astronomy) was founded by the Institute of Theoretical Physics and Astronomy (Lithuania) in 1992 and acquired by De Gruyter in 2016.