Abstract
Modified gravity with nonlocal term \(R^{-1}\mathcal{F}(\square )R,\) and without matter, is considered from the cosmological point of view. Equations of motion are derived. Cosmological solutions of the form \(a(t) = a_{0}\vert t - t_{0}\vert ^{\alpha },\) for the FLRW metric and k = 0, ±1, are found.
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References
Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Modified gravity and cosmology. Phys. Rep. 513, 1–189 (2012). arXiv:1106.2476v2 [astro-ph.CO]
Nojiri, S., Odintsov, S.D.: Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models. Phys. Rep. 505, 59–144 (2011). arXiv:1011.0544v4 [gr-qc]
Woodard, R.P.: Nonlocal models of cosmic acceleration (2014). arXiv:1401.0254 [astro-ph.CO]
Dragovich, B.: On nonlocal modified gravity and cosmology (in this volume)
Biswas, T., Mazumdar, A., Siegel, W: Bouncing universes in string-inspired gravity. J. Cosmol. Astropart. Phys. 0603, 009 (2006). arXiv:hep-th/0508194
Biswas, T., Koivisto, T., Mazumdar, A.: Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity. J. Cosmol. Astropart. Phys. 1011, 008 (2010). arXiv:1005.0590v2 [hep-th]
Biswas, T., Gerwick, E., Koivisto, T., Mazumdar, A.: Towards singularity and ghost free theories of gravity. Phys. Rev. Lett. 108, 031101 (2012). arXiv:1110.5249v2 [gr-qc]
Biswas, T., Koshelev, A.S., Mazumdar, A., Vernov, S.Y.: Stable bounce and inflation in non-local higher derivative cosmology. J. Cosmol. Astropart. Phys. 08, 024 (2012). arXiv:1206.6374 [astro-ph.CO]
Koshelev, A.S., Vernov, S.Y.: On bouncing solutions in non-local gravity (2012). arXiv:1202.1289v1 [hep-th]
Dimitrijevic, I., Dragovich, B., Grujic J., Rakic, Z.: On modified gravity. In: Dobrev, V. (ed.) Springer Proceedings in Mathematics and Statistics, vol. 36. Springer, Tokyo/Heidelberg (2013). arXiv:1202.2352 [hep-th]
Dimitrijevic, I., Dragovich, B., Grujic J., Rakic, Z.: New cosmological solutions in nonlocal modified gravity. Rom. J. Phys. 58(5–6), 550–559 (2013). arXiv:1302.2794 [gr-qc]
Biswas, T., Conroy, A., Koshelev, A.S., Mazumdar, A.: Generalized gost-free quadratic curvature gravity (2013). arXiv:1308.2319 [hep-th]
Dimitrijevic, I., Dragovich, B., Grujic J., Rakic, Z.: A new model of nonlocal modified gravity. Publications de l’Institut Mathematique 94(108), 187–196 (2013)
Erickcek, A.L., Smith, T.L., Kamionkowski M.: Solar system tests do rule out 1/R gravity. Phys. Rev. D74, 121501 (2006). arXiv:astro-ph/0610483
Deser, S., Woodard, R.P.: Nonlocal cosmology. Phys. Rev. Lett. 99, 111301 (2007). arXiv:0706.2151v2 [astro-ph]
Nojiri, S., Odintsov, S.D.: Modified non-local-F(R) gravity as the key for inflation and dark energy. Phys. Lett. B659, 821–826 (2008). arXiv:0708.0924v3 [hep-th]
Elizalde, E., Pozdeeva, E.O., Vernov, S.Y., Zhang, Y.: Cosmological solutions of a nonlocal model with a perfect fluid. J. Cosmol. Astropart. Phys. 1307, 034 (2013). arXiv:1302.4330v2 [hep-th]
Briscese, F., Marciano, A., Modesto, L., Saridakis, E.N.: Inflation in (super-)renormalizable gravity. Phys. Rev. D 87, 083507 (2013). arXiv:1212.3611v2 [hep-th]
Calcagni, G., Modesto, L., Nicolini, P.: Super-accelerting bouncing cosmology in assymptotically-free non-local gravity (2013). arXiv:1306.5332 [gr-qc]
Acknowledgements
Work on this paper was supported by Ministry of Education, Science and Technological Development of the Republic of Serbia, grant No. 174012. The authors thank Prof. V. Dobrev for invitation and hospitality at the X International Workshop “Lie Theory and its Applications in Physics”, 17–23 June 2013, Varna, Bulgaria.
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Dimitrijevic, I., Dragovich, B., Grujic, J., Rakic, Z. (2014). Some Power-Law Cosmological Solutions in Nonlocal Modified Gravity. In: Dobrev, V. (eds) Lie Theory and Its Applications in Physics. Springer Proceedings in Mathematics & Statistics, vol 111. Springer, Tokyo. https://doi.org/10.1007/978-4-431-55285-7_16
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DOI: https://doi.org/10.1007/978-4-431-55285-7_16
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