×

On modified gravity. (English) Zbl 1273.83145

Dobrev, Vladimir (ed.), Lie theory and its applications in physics. IX international workshop. Based on the 9th workshop on Lie theory and its applications in physics, Varna, Bulgaria, June 20–26, 2011. Tokyo: Springer (ISBN 978-4-431-54269-8/hbk; 978-4-431-54270-4/ebook). Springer Proceedings in Mathematics & Statistics 36, 251-259 (2013).
Summary: We consider some aspects of nonlocal modified gravity, where nonlocality is of the type \(R\mathcal{F}(\square )R\). In particular, using Ansatz of the form \(\square R = cR^{\gamma}\), we find a few special cosmological solutions for the spatially flat FLRW metric. There are singular and nonsingular bounce solutions. For late cosmic time, scalar curvature \(R(t)\) is in low regime and scale factor \(a(t)\) is decelerated.
For the entire collection see [Zbl 1266.00027].

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Modified gravity and cosmology [arXiv:1106.2476v2 [astro-ph.CO]]
[2] Modesto, L.: Super-renormalizable quantum gravity [arXiv:1107.2403v1 [hep-th]] · Zbl 1342.83087
[3] Sotiriou, T. P.; Faraoni, V., f(R) theories of gravity, Rev. Mod. Phys., 82, 451-497 (2010) · Zbl 1205.83006
[4] 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)
[5] Biswas, T.; Koivisto, T.; Mazumdar, A., Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity, J. Cosmology Astropart. Phys., 1011, 008 (2010)
[6] Aref’eva, I. Ya.; Joukovskaya, L. V.; Vernov, S. Yu., Bouncing and accelerating solutions in nonlocal stringy models, J. High Energy Phys., 0707, 087 (2007)
[7] Calcagni, G., Montobbio, M., Nardelli, G.: A route to nonlocal cosmology. Phys. Rev. D 76, 126001 (2007) [arXiv:0705.3043v3 [hep-th]] · Zbl 1282.81143
[8] Barnaby, N.; Biswas, T.; Cline, J. M., p-Adic inflation, J. High Energy Phys., 0704, 056 (2007)
[9] Koshelev, A. S.; Vernov, S. Yu., Analysis of scalar perturbations in cosmological models with a non-local scalar field, Class. Quant. Gravit., 28, 085019 (2011) · Zbl 1216.83060
[10] Calcagni, G., Nardelli, G.: Nonlocal gravity and the diffusion equation. Phys. Rev. D 82, 123518 (2010) [arXiv:1004.5144v2 [hep-th]] · Zbl 1189.83094
[11] Koshelev, A.S.: Modified non-local gravity [arXiv:1112.6410v1 [hep-th]]
[12] Koshelev, A.S., Vernov, S.Yu.: On bouncing solutions in non-local gravity [arXiv:1202.1289v1 [hep-th]] · Zbl 1216.83060
[13] Biswas, T.; Mazumdar, A.; Siegel, W., Bouncing universes in string-inspired gravity, J. Cosmology Astropart. Phys., 0603, 009 (2006) · Zbl 1236.83020 · doi:10.1088/1475-7516/2006/03/009
[14] Dragovich, B., Nonlocal dynamics of p-adic strings, Theor. Math. Phys., 164, 3, 1151-115 (2010) · Zbl 1254.81072
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.