Publication: Tidal forces in f(R) theories of gravity
Loading...
Full text at PDC
Publication Date
2014-01-01
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
APS
Citations
Exportar
Abstract
Despite the extraordinary attention that modified gravity theories have attracted over the past decade, the geodesic deviation equation in this context has not received proper formulation thus far. This equation provides an elegant way to investigate the timelike, null and spacelike structure of spacetime geometries.
In this investigation we provide the full derivation of this equation in situations where general relativity has been extended in Robertson-Walker background spacetimes. We find that for null geodesics the contribution arising from the geometrical new terms is in general nonzero. Finally we apply the results to a well-known class of f(R) theories, compare the results with general relativity predictions and obtain the equivalent area distance relation.
Description
UCM subjects
Unesco subjects
Keywords
Citation
[1] M. Chevallier and D. Polarski, Int. J. Mod. Phys. D 10, 213 (2001); D. Huterer andM. S. Turner, Phys. Rev. D 64, 123527 (2001); B.A.Bassett,M.Kunz, J. Silk, and C. Ungarelli,Mon. Not. R. Astron. Soc. 336, 1217 (2002); T. Padmanabhan and T. R. Choudhury, Mon. Not. R. Astron. Soc. 344, 823 (2003); D. A. Dicus and W.W. Repko, Phys. Rev. D 70, 083527 (2004); E.V. Linder, Phys. Rev. D 70, 023511 (2004); S. Hannestad and E. Mortsell, J. Cosmol. Astropart. Phys. 09 (2004) 001; P. S. Corasaniti, M. Kunz, D. Parkinson, E. J. Copeland, and B. A. Bassett, Phys. Rev. D 70, 083006 (2004).
[2] T. Clifton, P. G. Ferreira, A. Padilla, and C. Skordis, Phys. Rep. 513, 1 (2012).
[3] A. de Felice and S. Tsujikawa, Living Rev. Relativity 13, 3 (2010).
[4] L. Pogosian and A. Silvestri, Phys. Rev. D 77, 023503 (2008); Phys. Rev. D 81, 049901(E) (2010).
[5] J. A. R. Cembranos, Phys. Rev. D 73, 064029 (2006).
[6] B. Jain, V. Vikram, and J. Sakstein, Astrophys. J. 779, 39 (2013); L. Lombriser, A. Slosar, U. Seljak, andW. Hu, Phys. Rev. D 85, 124038 (2012); L. Lombriser, F. Schmidt, T. Baldauf, R. Mandelbaum, U. Seljak, and R. E. Smith, Phys. Rev. D 85, 102001 (2012); Y.-S. Song, H. Peiris, and W. Hu, Phys. Rev. D 76, 063517 (2007).
[7] S. M. Carroll, I. Sawicki, A. Silvestri, and M. Trodden, New J. Phys. 8, 323 (2006); Y. S. Song, W. Hu, and I. Sawicki, Phys. Rev. D 75, 044004 (2007); A.A. Starobinsky, JETP Lett. 86, 157 (2007); S. Carloni, P. K. S. Dunsby, and A. Troisi, Phys. Rev. D 77, 024024 (2008); A. de la Cruz-Dombriz, A. Dobado, and A. L. Maroto, Phys. Rev. D 77, 123515 (2008); Phys. Rev. Lett. 103, 179001 (2009); A. Abebe, M. Abdelwahab, A. de la Cruz-Dombriz, and P. K. S. Dunsby, Classical Quantum Gravity 29, 135011 (2012); J. Noller, F. von Braun-Bates, and P. G. Ferreira, Phys. Rev. D 89, 023521 (2014).
[8] H. Bourhrous, A. de la Cruz-Dombriz, and P. K. S. Dunsby, AIP Conf. Proc. 1458, 343 (2012);M. Abdelwahab, A. de la Cruz-Dombriz, and P. K. S. Dunsby, AIP Conf. Proc. 1514, 157 (2012); K. N. Ananda, S. Carloni, and P. K. S. Dunsby, Phys. Rev. D 77, 024033 (2008); M. Bouhmadi-Lopez, J. Morais, and A. B. Henriques, arXiv:1302.2038; N. Bevis, M. Hindmarsh, M. Kunz, and J. Urrestilla, Phys. Rev. D 75, 065015 (2007); J. Urrestilla, N. Bevis, M. Hindmarsh, and M. Kunz, J. Cosmol. Astropart. Phys. 12 (2011) 021; J. Urrestilla, N. Bevis, M. Hindmarsh, and M. Kunz, Phys. Rev. D 82, 065004 (2010); Phys. Rev. D 86, 023513 (2012); R. A. Battye, C. Van de Bruck, and A. Mennim, Phys. Rev. D 69, 064040 (2004); R. Easther, D. Langlois, R. Maartens, and D. Wands, J. Cosmol. Astropart. Phys. 10 (2003) 014; B. Leong, A. Challinor, R. Maartens, and A. Lasenby, Phys. Rev. D 66 104010 (2002); Y. Zhong, Y.-X. Liu, and K. Yang, Phys. Lett. B 699, 398 (2011).
[9] G. J. Olmo, Phys. Rev. D 75, 023511 (2007); A.M. Nzioki, S. Carloni, R. Goswami, and P. K. S. Dunsby, Phys. Rev. D 81, 084028 (2010); A. de la Cruz-Dombriz, A. Dobado, and A. L. Maroto, Phys. Rev. D 80, 124011 (2009); Phys. Rev. D 83, 029903(E) (2011); J. Phys. Conf. Ser. 229, 012033(2010); J. A. R. Cembranos, A. de la Cruz-Dombriz, and P. Jimeno Romero, Int. J. Geom. Methods Mod. Phys. 11, 1450001 (2014); AIP Conf. Proc. 1458, 439 (2012).
[10] A. de la Cruz-Dombriz and D. Sáez-Gómez, Classical Quantum Gravity, 29, 245014 (2012).
[11] G. F. R. Ellis and H. van Elst, arXiv:gr-qc/9709060v1.
[12] W. Mattig, Astron. Nachr. 284, 109 (1957).
[13] A. Raychaudhuri, Phys. Rev. 98, 1123 (1955).
[14] M. Sasaki, Mon. Not. R. Astron. Soc. 228, 653 (1987); T. Futamase and M. Sasaki, Phys. Rev. D 40, 2502 (1989); T. Pyne and M. Birkinshaw, Astrophys. J. 415, 459 (1993); S. Seitz, P. Schneider, and J. Ehlers, Classical Quantum Gravity 11, 2345 (1994); C. Clarkson, G. Ellis, A. Faltenbacher, R. Maartens, O. Umeh, and J.-P. Uzan, Mon. Not. R. Astron. Soc. 426, 1121 (2012).
[15] A. Guarnizo, L. Castaneda and J. M. Tejeiro, Gen. Relativ. Gravit. 43, 2713 (2011).
[16] F. Shojai and A. Shojai, Phys. Rev. D 78, 104011 (2008); G. J. Olmo, Int. J. Mod. Phys. D 20, 413 (2011); T. Harko, T. S. Koivisto, and F. S. N. Lobo, Mod. Phys.Lett.A26, 1467 (2011).
[17] T. Harko and F. S. N. Lobo, Phys. Rev. D 86, 124034 (2012).
[18] W. Hu and I. Sawicki, Phys. Rev. D 76, 064004 (2007).
[19] S. ’i. Nojiri and S. D. Odintsov, Phys. Rep. 505, 59 (2011); Int. J. Geom. Methods Mod. Phys. 04, 115 (2007); S. Tsujikawa, Phys. Rev. D 77, 023507 (2008); J.A.R. Cembranos, A. de la Cruz-Dombriz, and B. Montes Nunez, J. Cosmol. Astropart. Phys. 04 (2012) 021.
[20] V. Sahni and A. Starobinsky, Int. J. Mod. Phys. D 15, 2105 (2006).
[21] C. Clarkson and C. Zunckel, Phys. Rev. Lett. 104, 211301 (2010); E. E. O. Ishida and R. S. de Souza, Astron. Astrophys. 527, A49 (2011).
[22] M. Visser, Classical Quantum Gravity 21, 2603 (2004).
[23] M. Seikel, C. Clarkson, and M. Smith, J. Cosmol. Astropart. Phys. 06 (2012) 036; M. Seikel, S. Yahya, R. Maartens, and C. Clarkson, Phys. Rev. D 86, 083001 (2012).
[24] A. Aviles, A. Bravetti, S. Capozziello, and O. Luongo, Phys. Rev. D 87, 044012 (2013).
[25] S. Carloni, P. K. S. Dunsby, and A. Troisi, Phys. Rev. D 77, 024024 (2008).
[26] A. Friedman, Z. Phys. 10, 377 (1922); [Gen. Relativ. Gravit. 31, 1991 (1999)].
[27] J. A. Schouten, Ricci Calculus (Springer, Berlin, 1954).
[28] J. L. Synge and A. Schild, Tensor Calculus (Dover Publishing, New York, 1978).
[29] R. M. Wald, General Relativity (University of Chicago Press, Chicago, 1984).
[30] J. L. Synge, Ann. Math. 35, 705 (1934).
[31] J. L. Synge, General Relativity (North Holland, Amsterdam, 1960).
[32] J. Santos, J. S. Alcaniz, M. J. Reboucas, and F. C. Carvalho, Phys. Rev. D 76, 083513 (2007); J. Santos, M. J. Reboucas, and J. S. Alcaniz, Int. J. Mod. Phys. D 19, 1315 (2010).
[33] F. D. Albareti, J. A. R. Cembranos, A. de la Cruz-Dombriz, and A. Dobado, J. Cosmol. Astropart. Phys. 07 (2013) 009.
[34] D. R. Matravers and A. M. Aziz, Mon. Not. R. Astron. Soc. 47, 124 (1988).
[35] K. Tomita, H. Asada, and T. Hamana, Prog. Theor. Phys. Suppl. 133, 155 (1999).
[36] K. Tomita, H. Asada, and T. Hamana, Dynamical Systems in Cosmology edited by J. Wainwright and G. F. R. Ellis (Cambridge University Press, Cambridge, 2005).
[37] S. Carloni, P. K. S. Dunsby, S. Capozziello, and A. Troisi, Classical Quantum Gravity 22, 4839 (2005); S. Carloni and P. K. S. Dunsby, J. Phys. A 40, 6919 (2007); S. Carloni, A. Troisi, and P. K. S. Dunsby, Gen. Relativ. Gravit. 41, 1757 (2009); N. Goheer, J. A. Leach, and P. K. S. Dunsby, Classical Quantum Gravity 25, 035013 (2008); N. Goheer, J. A. Leach, and P. K. S. Dunsby, Classical Quantum Gravity 24, 5689 (2007); J. A. Leach, S. Carloni, and P. K. S. Dunsby, Classical Quantum Gravity 23, 4915 (2006); M. Abdelwahab, S. Carloni, and P. K. S. Dunsby, Classical Quantum Gravity 25, 135002 (2008); M. Abdelwahab, R. Goswami, and P. K. S. Dunsby, Phys. Rev. D 85, 083511 (2012).
[38] L. I. Gurvits, K. I. Kellerman, and S. Frey, Astron. Astrophys. 342, 378 (1999); J. A. S. Lima and J. S. Alcaniz, Astrophys. J. 566, 15 (2002); J. C. Jackson, Mon. Not. R. Astron. Soc. Lett. 390, L1 (2008).
[39] E. de Filippis, M. Sereno, M.W. Bautz, and G. Longo, Astrophys. J. 625, 108 (2005); M. Bonamente, M. K. Joy, S. J. LaRoque, J. E. Carlstrom, E. D. Reese, and K. S. Dawson, Astrophys. J. 647, 25 (2006); Y. Chen and B. Ratra, Astron. Astrophys. 543, A104 (2012); R.F.L. Holanda, J. S. Alcaniz, and J. C. Carvalho, J. Cosmol. Astropart. Phys. 06 (2013) 033.
[40] N. Suzuki et al., Astrophys. J. 746, 85 (2012); H. Campbell et al., Astrophys. J. 763, 88 (2013).
[41] C. C. Dyer and R. C. Roeder, Astrophys. J. 180, L31 (1973); V. C. Busti, R. C. Santos, and J. A. S. Lima, Phys. Rev. D 85, 103503 (2012); V. C. Busti, R. F. L. Holanda, and C. Clarkson, J. Cosmol. Astropart. Phys. 11 (2013) 020.