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On Nonlocal Modified Gravity and Its Cosmological Solutions

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Lie Theory and Its Applications in Physics (LT 2015)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 191))

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Abstract

During hundred years of General Relativity (GR), many significant gravitational phenomena have been predicted and discovered. General Relativity is still the best theory of gravity. Nevertheless, some (quantum) theoretical and (astrophysical and cosmological) phenomenological difficulties of modern gravity have been motivation to search more general theory of gravity than GR. As a result, many modifications of GR have been considered. One of promising recent investigations is Nonlocal Modified Gravity. In this article we present a brief review of some nonlocal gravity models with their cosmological solutions, in which nonlocality is expressed by an analytic function of the d’Alembert-Beltrami operator \(\Box \). Some new results are also presented.

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Notes

  1. 1.

    While we prepared this contribution, the discovery of gravitational waves was announced [1].

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Acknowledgements

Work on this paper was partially supported by Ministry of Education, Science and Technological Development of the Republic of Serbia, grant No 174012. B.D. thanks Prof. Vladimir Dobrev for invitation to participate and give a talk on nonlocal gravity, as well as for hospitality, at the XI International Workshop “Lie Theory and its Applications in Physics”, 15–21 June 2015, Varna, Bulgaria. B.D. also thanks a support of the ICTP - SEENET-MTP project PRJ-09 “Cosmology and Strings” during preparation of this article. AK is supported by the FCT Portugal fellowship SFRH/BPD/105212/2014 and in part by FCT Portugal grant UID/MAT/00212/2013 and by RFBR grant 14-01-00707.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Belgrade, Studentski Trg 16, Belgrade, Serbia

    Ivan Dimitrijevic & Zoran Rakic

  2. Institute of Physics, University of Belgrade, Belgrade, Serbia

    Branko Dragovich

  3. Mathematical Institute SANU, Belgrade, Serbia

    Branko Dragovich

  4. Teacher Education Faculty, University of Belgrade, Kraljice Natalije 43, Belgrade, Serbia

    Jelena Stankovic

  5. Departamento de Física and Centro de Matemática e Aplicações, Universidade da Beira Interior, 6200, Covilhã, Portugal

    Alexey S. Koshelev

  6. Theoretische Natuurkunde, Vrije Universiteit Brussel, and The International Solvay Institutes, Pleinlaan 2, 1050, Brussels, Belgium

    Alexey S. Koshelev

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  1. Ivan Dimitrijevic
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  2. Branko Dragovich
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  3. Jelena Stankovic
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  4. Alexey S. Koshelev
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Correspondence to Branko Dragovich .

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Editors and Affiliations

  1. Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vladimir Dobrev

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Dimitrijevic, I., Dragovich, B., Stankovic, J., Koshelev, A.S., Rakic, Z. (2016). On Nonlocal Modified Gravity and Its Cosmological Solutions. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. LT 2015. Springer Proceedings in Mathematics & Statistics, vol 191. Springer, Singapore. https://doi.org/10.1007/978-981-10-2636-2_3

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