Publication:
Large scale structure constraints for a class of f(R) theories of gravity

Loading...
Thumbnail Image
Full text at PDC
Publication Date
2013-08-26
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Citations
Google Scholar
Research Projects
Organizational Units
Journal Issue
Abstract
Over the past few years much attention has been given to the study of modified gravity theories in order to find a more natural explanation for the late time acceleration of the Universe. Nevertheless, a comparison of the matter power spectrum predictions made by these theories with available data has not yet been subjected to a detailed analysis. In the context of f(R) theories of gravity we study the predicted power spectra using both a dynamical systems approach for the background and solving for the matter perturbations without using the quasistatic approximation, comparing the theoretical results with several Sloan Digital Sky Survey data. The importance of studying the first order perturbed equations by assuming the correct background evolution and the relevance of the initial conditions are also stressed. We determine the statistical significance in relation to the observational data and demonstrate their conflict with existing observations.
Description
© 2013 American Physical Society. We would like to thank David Bacon for a comprehensive reading of the manuscript and for his useful comments. We are also indebted to Marc Manera and Ashley Ross for providing us the most updated literature about the SDSS-III project. We warmly thank as well José Beltrán for useful comments about BAO calculations. A. A. acknowledges financial support from NRF (South Africa). A. d. l. C. D. acknowledges financial support from Marie Curie–Beatriu de Pinós Contract No. BP-B00195 Generalitat de Catalunya, ACGC University of Cape Town and MINECO (Spain) Projects No. FIS2011-23000, No. FPA2011-27853-C02-01 and Consolider-Ingenio MULTIDARK Grant No. CSD2009-00064. P. K. S. D. thanks the NRF for financial support and Queen Mary, University of London for support during the final stages of this work. A. d. l. C. D. thanks the KITPC, Chinese Academy of Sciences, for its hospitality during the final stages of this work.
Unesco subjects
Keywords
Citation
[1] J. P. Ostriker and P. J. Steinhardt, arXiv:astro-ph/9505066. [2] S. Perlmutter et al., Astrophys. J. 517, 565 (1999); A.G. Riess et al., Astron. J. 116, 1009 (1998); J. L. Tonry et al., Astrophys. J. 594, 1 (2003); R.A. Knop et al., Astrophys. J. 598, 102 (2003); A.G. Riess et al., Astrophys. J. 607, 665 (2004); S. Perlmutter et al., Astrophys. J. 517, 565 (1999); Astron. Astrophys. 447, 31 (2006). [3] D. N. Spergel et al., Astrophys. J. Suppl. Ser. 148, 175 (2003); D.N. Spergel et al., Astrophys. J. Suppl. Ser. 170, 377 (2007). [4] M. Tegmark et al., Phys. Rev. D 69, 103501 (2004); U. Seljak et al., Phys. Rev. D 71, 103515 (2005); S. Cole et al., Mon. Not. R. Astron. Soc. 362, 505 (2005). [5] D. J. Eisenstein et al., Astrophys. J. 633, 560 (2005); C. Blake, D. Parkinson, B. Bassett, K. Glazebrook, M. Kunz, and R. C. Nichol, Mon. Not. R. Astron. Soc. 365, 255 (2006). [6] B. Jain and A. Taylor, Phys. Rev. Lett. 91, 141302 (2003). [7] A. A. Starobinsky, Phys. Lett. 91B, 99 (1980); K. S. Stelle, Gen. Relativ. Gravit. 9, 353 (1978). [8] S. M. Carroll, V. Duvvuri, M. Trodden, and M. S. Turner, Phys. Rev. D 70, 043528 (2004); S. Nojiri and S.D. Odintsov, Phys. Rev. D 68, 123512 (2003); S. Capozziello, Int. J.Mod. Phys. D 11, 483 (2002); V. Faraoni, Phys. Rev. D 72, 124005 (2005); M.L. Ruggiero and L. Iorio, J. Cosmol. Astropart. Phys. 01 (2007) 010; N. J. Poplawski, Phys. Rev. D 74, 084032 (2006); Classical Quantum Gravity 24, 3013 (2007); A.W. Brookfield, C. van de Bruck, and L.M.H. Hall, Phys. Rev. D 74, 064028 (2006); Y. Song,W. Hu, and I. Sawicki, Phys. Rev. D 75, 044004 (2007); B. Li, K. Chan, and M. Chu, Phys. Rev. D 76, 024002 (2007); X. Jin, D. Liu, and X. Li, arXiv:astro-ph/0610854; T. P. Sotiriou and S. Liberati, Ann Phys. (Amsterdam) 322, 935 (2007); Classical Quantum Gravity 23, 5117 (2006); R. Bean, D. Bernat, L. Pogosian, A. Silvestri, and M. Trodden, Phys. Rev. D 75, 064020 (2007); I. Navarro and K. Van Acoleyen, J. Cosmol. Astropart. Phys. 02 (2007) 022; A.J. Bustelo and D. E. Barraco, Classical Quantum Gravity 24, 2333 (2007); G. J. Olmo, Phys. Rev. D 75, 023511 (2007); J. Ford, S. Giusto, and A. Saxena, Nucl. Phys. B790, 258 (2008); F. Briscese, E. Elizalde, S. Nojiri, and S.D. Odintsov, Phys. Lett. B 646, 105 (2007); S. Baghram, M. Farhang, and S. Rahvar, Phys. Rev. D 75, 044024 (2007); D. Bazeia, B. Carneiro da Cunha, R. Menezes, and A.Yu. Petrov, Phys. Lett. B 649, 445 (2007); P. Zhang, Phys. Rev. D 76, 024007 (2007); B. Li and J.D. Barrow, Phys. Rev. D 75, 084010 (2007); T. Rador, Phys. Lett. B 652, 228 (2007); Phys. Rev. D 75, 064033 (2007); L.M. Sokolowski, Classical Quantum Gravity 24, 3391 (2007); V. Faraoni, Phys. Rev. D 75, 067302 (2007); O. Bertolami, C.G. Boehmer, T. Harko, and F. S.N. Lobo, Phys. Rev. D 75, 104016 (2007); S.K. Srivastava, Int. J. Theor. Phys. 47, 1966 (2008); S. Capozziello, V. F. Cardone, and A. Troisi, J. Cosmol. Astropart. Phys. 08 (2006) 001; A.A. Starobinsky, JETP Lett. 86, 157 (2007); A. De Felice and S. Tsujikawa, Living Rev. Relativity 13, 3 (2010); S. Capozziello and M. De Laurentis, Phys. Rep. 509, 167 (2011). [9] R. Kerner, Gen. Relativ. Gravit. 14, 453 (1982); J.P. Duruisseau and R. Kerner, Classical Quantum Gravity 3, 817 (1986). [10] P. Teyssandier, Classical Quantum Gravity 6, 219 (1989). [11] G. Magnano, M. Ferraris, and M. Francaviglia, Gen. Relativ. Gravit. 19, 465 (1987). [12] S. Capozziello, V. F. Cardone, S. Carloni, and A. Troisi, Int. J. Mod. Phys. D 12, 1969 (2003). [13] K. i. Maeda and N. Ohta, Phys. Lett. B 597, 400 (2004); Phys. Rev. D 71, 063520 (2005); K. Akune, K. i. Maeda, and N. Ohta, Phys. Rev. D 73, 103506 (2006). [14] S. Capozziello, V. F. Cardone, and A. Troisi, Mon. Not. R. Astron. Soc. 375, 1423 (2007). [15] K. Bamba, A. Lopez-Revelles, R. Myrzakulov, S.D. Odintsov, and L. Sebastiani, Classical Quantum Gravity 30, 015008 (2013); J.A.R. Cembranos, A. de la Cruz-Dombriz, and P. J. Romero, Entropy 14, 1717 (2012); S.A. Appleby, R.A. Battye, and A. A. Starobinsky, J. Cosmol. Astropart. Phys. 06 (2010) 005; K. Bamba, C.-Q. Geng, and C.-C. Lee, Int. J. Mod. Phys. D 20, 1339 (2011); L. Reverberi, Phys. Rev. D 87, 084005 (2013); J.A.R. Cembranos, A. de la Cruz-Dombriz, and B. Montes Nunez, J. Cosmol. Astropart. Phys. 04 (2012) 021; D. Sáez-Gómez, AIP Conf. Proc. 1514, 187 (2012); A. de la Cruz-Dombriz and D. Sáez-Gómez, Classical Quantum Gravity 29, 245014 (2012); Entropy 14, 1717 (2012); S. Nojiri and S. D. Odintsov, Phys. Rev. D 78, 046006 (2008); K. Bamba, C. Q. Geng, S. Nojiri, and S. D. Odintsov, Mod. Phys. Lett. A 25, 900 (2010); Phys. Rev. D 79, 083014 (2009); A. de la Cruz-Dombriz, A. Dobado, and A. L. Maroto, Phys. Rev. D 80, 124011 (2009); 83, 029903(E) (2011); L. Fernández-Jambrina and R. Lazkoz, Phys. Lett. B 670, 254 (2009); K. Bamba, S. Nojiri, and S. D. Odintsov, J. Cosmol. Astropart. Phys. 10 (2008) 045; H. Motohashi, A. A. Starobinsky, and J. ’i. Yokoyama, J. Cosmol. Astropart. Phys. 06 (2011) 006; E.V. Arbuzova and A. D. Dolgov, Phys. Lett. B 700, 289 (2011); R. Goswami, N. Goheer, and P. K. S. Dunsby, Phys. Rev. D 78, 044011S (2008); S. Carloni, P. K. S. Dunsby, and D. M. Solomons, Classical Quantum Gravity 23, 1913 (2006); O. Mena, J. Santiago, and J. Weller, Phys. Rev. Lett. 96, 041103 (2006). [16] Dynamical Systems in Cosmology, edited by J.Wainwright and G. F. R. Ellis (Cambridge University Press, Cambridge, 2005), ISBN 0-521-55457-8. [17] 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); 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). [18] A. de la Cruz-Dombriz and A. Dobado, Phys. Rev. D 74, 087501 (2006). [19] N. Goheer, J. Larena, and P. K. S. Dunsby, Phys. Rev. D 80, 061301 (2009). [20] P. K. S. Dunsby, E. Elizalde, R. Goswami, S. Odintsov, and D. Sáez-Gómez, Phys. Rev. D 82, 023519 (2010). [21] S. Nojiri, S. D. Odintsov, A. Toporensky, and P. Tretyakov, Gen. Relativ. Gravit. 42, 1997 (2010); G. Cognola, E. Elizalde, S. Nojiri, and S. D. Odintsov, Open Astron. J. 3, 20 (2010); S. Nojiri, S. D. Odintsov, and D. Sáez-Gómez, Phys. Lett. B 681, 74 (2009); S. Nojiri and S. D. Odintsov, J. Phys. Conf. Ser. 66, 012005 (2007); Phys. Rev. D 74, 086005 (2006); S. Nojiri, S. D. Odintsov, and M. Sami, Phys. Rev. D 74, 046004 (2006); E. Elizalde, R. Myrzakulov, V.V. Obukhov, and D. Sáez-Gómez, Classical Quantum Gravity 27, 095007 (2010). [22] S. Carloni, R. Goswami, and P. K. S. Dunsby, Classical Quantum Gravity 29, 135012 (2012). [23] A. de la Cruz-Dombriz, A. Dobado, and A. L. Maroto, Phys. Rev. D 77, 123515 (2008); AIP Conf. Proc. 1122, 252 (2009). [24] H. Motohashi, A. A. Starobinsky, and J. ’i. Yokoyama, Int. J. Mod. Phys. D 18, 1731 (2009). [25] A. Hojjati, L. Pogosian, A. Silvestri, and S. Talbot, Phys. Rev. D 86, 0123503 (2012). [26] R. Bean, D. Bernat, L. Pogosian, A. Silvestri, and M. Trodden, Phys. Rev. D 75, 064020 (2007). [27] J. M. Bardeen, Phys. Rev. D 22, 1882 (1980). [28] G. F. R. Ellis and M. Bruni, Phys. Rev. D 40, 1804 (1989); M. Bruni, P. K. S. Dunsby, and G. F. R. Ellis, Astrophys. J. 395, 34 (1992); P.K. S. Dunsby, M. Bruni, and G. F. R. Ellis, Astrophys. J. 395, 54 (1992); M. Bruni, G. F. R. Ellis, and P. K. S. Dunsby, Classical Quantum Gravity 9, 921 (1992); P.K. S. Dunsby, Classical Quantum Gravity 8, 1785 (1991); J. Hwang, Phys. Rev. D 42, 2601 (1990); P. K. S. Dunsby, Phys. Rev. D 48, 3562 (1993); Classical Quantum Gravity 14, 3391 (1997); T. Gebbie, P. Dunsby, and G. F. R. Ellis, Ann. Phys. (N.Y.) 282, 321 (2000); P. K. S. Dunsby, Ph.D. thesis, Queen Mary and Westfield College, London, 1992. [29] S. Carloni, P. K. S. Dunsby, and A. Troisi, Phys. Rev. D 77, 024024 (2008); K.N. Ananda, S. Carloni, and P. K. S. Dunsby, Phys. Rev. D 77, 024033 (2008); Classical Quantum Gravity 26, 235018 (2009); A. Abebe, M. Abdelwahab, A. de la Cruz-Dombriz, and P. K. S. Dunsby, Classical Quantum Gravity 29, 135011 (2012). [30] K. N. Ananda, S. Carloni, and P. K. S. Dunsby, arXiv:0812.2028. [31] P. Zhang, Phys. Rev. D 73, 123504 (2006). [32] A. de la Cruz-Dombriz, A. Dobado, and A. L. Maroto, Phys. Rev. Lett. D 103, 179001 (2009). [33] P. K. S. Dunsby, M. Bruni, and G. F. R. Ellis, Astrophys. J. 395, 54 (1992). [34] E. Bertschinger and P. Zukin, Phys. Rev. D 78, 024015 (2008). [35] E.V. Linder and R. N. Cahn, Astropart. Phys. 28, 481 (2007); G.-B. Zhao, L. Pogosian, A. Silvestri, and J. Zylberberg, Phys. Rev. D 79, 083513 (2009); A. Hojjati, L. Pogosian, and G. Zhao, J. Cosmol. Astropart. Phys. 08 (2011) 005; http://www.sfu.ca/~aha25/MGCAMB.html; T. Giannantonio, M. Martinelli, A. Silvestri, and A. Melchiorri, J. Cosmol. Astropart. Phys. 04 (2010) 030; R. Bean and M. Tangmatitham, Phys. Rev. D 81, 083534 (2010); B. Hu, M. Liguori, N. Bartolo, and S. Matarrese, arXiv:1307.5276; A. Marchini and V. Salvatelli, arXiv:1307.2002. [36] E. Di Dio, F. Montanari, J. Lesgourgues, and R. Durrer, arXiv:1307.1459. [37] http://space.mit.edu/home/tegmark/sdss.html; M. Tegmark et al. (SDSS Collaboration), Phys. Rev. D 74, 123507 (2006). [38] A. J. Ross et al. (BOSS Collaboration), Mon. Not. R. Astron. Soc. 424, 564 (2012). [39] A. Friedman, Z. Phys. 10, 377 (1922) [Gen. Relativ. Gravit. 31, 1991 (1999)]; A. Raychaudhuri, Phys. Rev. 98, 1123 (1955). [40] P. Coles and F. Lucchin, Cosmology: The Origin and Evolution of Cosmic Structure (Wiley, Chichester, UK, 1995). [41] T. Padmanabhan, AIP Conf. Proc. 843, 111 (2006); Structure Formation in the Universe (Cambridge University Press, Cambridge, UK, 1993), ISBN 0-521- 42486-0. [42] C. Blake et al., Mon. Not. R. Astron. Soc. 418, 1707 (2011). [43] R. Lazkoz, S. Nesseris, and L. Perivolaropoulos, J. Cosmol. Astropart. Phys. 08 (2008) 012. [44] P. A. R. Ade et al. (PLANCK Collaboration), arXiv:1303.5076. [45] A. Marchini and V. Salvatelli, Phys. Rev. D 88, 027502 (2013). [46] F. Beutler, C. Blake, M. Colless, D. Heath Jones, L. S. Smith, L. Campbell, Q. Parker, W. Saunders, and F. Watson, Mon. Not. R. Astron. Soc. 416, 3017 (2011). [47] W. J. Percival et al. (SDSS Collaboration), Mon. Not. R. Astron. Soc. 401, 2148 (2010). [48] N. Padmanabhan, X. Xu, D. J. Eisenstein, R. Scalzo, A. J. Cuesta, K. T. Mehta, and E. Kazin, Mon. Not. R. Astron. Soc. 427, 2132 (2012). [49] L. Anderson et al., Mon. Not. R. Astron. Soc. 427, 3435 (2013). [50] T. Clifton and J. D. Barrow, Phys. Rev. D 72, 103005 (2005).
Collections