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Evolution of the equations of dynamics of the Universe: From Friedmann to the present day

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Abstract

Celebrating the centenary of general relativity theory, we must recall that Friedmann’s discovery of the equations of evolution of the Universe became the strongest prediction of this theory. These equations currently remain the foundation of modern cosmology. Nevertheless, data from new observations stimulate a search for modified theories of gravitation. We discuss cosmological aspects of theories with two dynamical metrics and theories of massive gravity, one of which was developed by Logunov and his coworkers.

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References

  1. A. Friedmann, “Letters and manuscripts,” In the P. Ehrenfest archive, http://www.lorentz.leidenuniv.nl/history/Friedmann archive/ (1922).

    Google Scholar 

  2. A. Friedmann, “Über die Krümmung des Raumes,” Z. Phys., 10, 377–386 (1922).

    Article  ADS  MATH  Google Scholar 

  3. Yu. Tsipenyuk, “How I remember P. L. Kapitza [in Russian],” Kvant, 5–6, 23–25 (2014).

    Google Scholar 

  4. G. Gamov, The Creation of the Universe, Viking, New York (1952).

    Google Scholar 

  5. A. Einstein, “Näherungsweise Integration der Feldgleichungen der Gravitation,” Sitzungsber. Preuss. Akad. Wiss. (Berlin), 1, 688–696 (1916).

    MATH  Google Scholar 

  6. P. A. M. Dirac, “Fixation of coordinates in the Hamiltonian theory of gravitation,” Phys. Rev., 114, 924–930 (1959).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. R. Arnowitt, S. Deser, and Ch. W. Misner, Gravitation: An Introduction to Current Research, Wiley (1962).

    Google Scholar 

  8. B. S. DeWitt, “The quantum theory of gravity: I. The canonical theory,” Phys. Rev., 160, 1113–1148 (1967).

    Article  ADS  MATH  Google Scholar 

  9. M. Ryan, Hamiltonian Cosmology, Springer, Berlin (1972).

    Google Scholar 

  10. A. A. Logunov, Relativistic Theory of Gravitation [in Russian], Nauka, Moscow (2012).

    MATH  Google Scholar 

  11. S. S. Gershtein, A. A. Logunov, and M. A. Mestvirishvili, “On an upper limit for graviton mass,” Dokl. Phys., 43, 293–296 (1998); arXiv:hep-th/9711147v1 (1997).

    ADS  MathSciNet  Google Scholar 

  12. C. de Rham, G. Gabadadze, and A. J. Tolley, “Resummation of massive gravity,” Phys. Rev. Lett., 106, 231101 (2011); arXiv:1011.1232v2 [hep-th (2010).

    Article  ADS  Google Scholar 

  13. D. Boulware and S. Deser, “Can gravitation have a finite range?” Phys. Rev. D, 6, 3368–3382 (1972).

    Article  ADS  Google Scholar 

  14. C. de Rham, L. Heisenberg, and R. H. Ribeiro, “On couplings to matter in massive (bi-)gravity,” Class. Q. Grav., 32, 035022 (2015); arXiv:1408.1678v3 [hep-th] (2014).

    Article  ADS  MATH  Google Scholar 

  15. M. Lagos and J. Noller, “New massive bigravity cosmologies with double matter coupling,” JCAP, 1601, 023 (2016); arXiv:1508.05864v2 [gr-qc] (2015).

    Article  ADS  MathSciNet  Google Scholar 

  16. A. R. Solomon, J. Enander, Y. Akrami, T. S. Koivisto, F. König, and E. Mörtsell, “Cosmological viability of massive gravity with generalized matter coupling,” JCAP, 1504, 027 (2015); arXiv:1409.8300v3 [astro-ph.CO] (2014).

    Article  ADS  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Institute for High Energy Physics, National Research Center “Kurchatov Institute”, Protvino, Moscow Oblast, Russia

    V. O. Soloviev

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  1. V. O. Soloviev
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Correspondence to V. O. Soloviev.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 191, No. 2, pp. 234–242, May, 2017.

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Soloviev, V.O. Evolution of the equations of dynamics of the Universe: From Friedmann to the present day. Theor Math Phys 191, 674–681 (2017). https://doi.org/10.1134/S0040577917050087

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