Publication: On the non-attractive character of gravity in f(R) theories
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2013-07
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Abstract
Raychaudhuri equation is found provided that particular energy conditions are assumed and regardless the considered solution of the Einstein's equations. This fact is usually interpreted as a manifestation of the attractive character of gravity. Nevertheless, a positive contribution to Raychaudhuri equation from space-time geometry should occur since this is the case in an accelerated expanding Robertson-Walker model for congruences followed by fundamental observers. Modified gravity theories provide the possibility of a positive contribution although the standard energy conditions are assumed. We address this important issue in the context of f(R) theories, deriving explicit upper bounds for the contribution of space-time geometry to the Raychaudhuri equation. Then, we examine the parameter constraints for some paradigmatic f(R) models in order to ensure a positive contribution to this equation. Furthermore, we consider the implications of these upper bounds in the equivalent formulation of f(R) theories as a Brans-Dicke model.
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©2013 IOP Publishing Ltd and Sissa Medialab srl
This work has been supported by MINECO (Spain) project numbers FIS2011-23000, FPA2011-27853-C02-01 and Consolider-Ingenio MULTIDARK CSD2009-00064. AdlCD also acknowledges financial support from Marie Curie - Beatriu de Pinós contract BP-B00195, Generalitat de Catalunya and ACGC, University of Cape Town.
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[1] Supernova Search Team collaboration, A.G. Riess et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 (1998) 1009 [astro-ph/9805201] [INSPIRE];
Supernova Cosmology Project collaboration, S. Perlmutter et al., Measurements of Omega and Lambda from 42 high redshift supernovae, Astrophys. J. 517 (1999) 565 [astro-ph/9812133] [INSPIRE];
Supernova Search Team collaboration, J.L. Tonry et al., Cosmological results from high-z supernovae, Astrophys. J. 594 (2003) 1 [astro-ph/0305008] [INSPIRE].
[2] A. Dobado and A.L. Maroto, Some consequences of the effective low-energy Lagrangian for gravity, Phys. Lett. B 316 (1993) 250 [Erratum ibid. B 321 (1994) 435] [hep-ph/9309221] [INSPIRE];
S. Nojiri and S.D. Odintsov, Introduction to modified gravity and gravitational alternative for dark energy, eConf C 0602061 (2006) 06 [Int. J. Geom. Meth. Mod. Phys. 4 (2007) 115] [hep-th/0601213] [INSPIRE] [INSPIRE];
S. Nojiri and S.D. Odintsov, Unied cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models, Phys. Rept. 505 (2011) 59 [arXiv:1011.0544] [INSPIRE];
S. Capozziello and M. Francaviglia, Extended Theories of Gravity and their Cosmological and Astrophysical Applications, Gen. Rel. Grav. 40 (2008) 357 [arXiv:0706.1146] [INSPIRE];
T.P. Sotiriou and V. Faraoni, f(R) Theories Of Gravity, Rev. Mod. Phys. 82 (2010) 451 [arXiv:0805.1726] [INSPIRE];
F.S. Lobo, The Dark side of gravity: Modified theories of gravity, arXiv:0807.1640 [INSPIRE]; S. Capozziello and V. Faraoni, Fundamental Theories of Physics. Vol. 170: Beyond Einstein Gravity, Springer, Dordrecht Netherlands (2011).
[3] C. Lanczos, Electromagnetism as a natural Property of Riemannian Geometry, Z. Phys. 73 (1932) 147;
C. Lanczos, A remarkable property of the Riemann-Christo el tensor in four dimensions, Ann.Math. 39 (1938) 842;
D. Lovelock, The Einstein tensor and its generalizations, J. Math. Phys. 12 (1971) 498 [INSPIRE].
[4] G. Cognola, E. Elizalde, S. Nojiri, S.D. Odintsov and S. Zerbini, Dark energy in modified Gauss-Bonnet gravity: Late-time acceleration and the hierarchy problem, Phys. Rev. D 73 (2006) 084007 [hep-th/0601008] [INSPIRE];
S. Nojiri and S.D. Odintsov, Modified Gauss-Bonnet theory as gravitational alternative for dark energy, Phys. Lett. B 631 (2005) 1 [hep-th/0508049] [INSPIRE];
S. Nojiri and S.D. Odintsov, Modified gravity with negative and positive powers of the curvature: Unication of the inflation and of the cosmic acceleration, Phys. Rev. D 68 (2003) 123512 [hep-th/0307288] [INSPIRE];
E. Elizalde, R. Myrzakulov, V. Obukhov and D. S aez-G omez, LambdaCDM epoch reconstruction from F(R;G) and modied Gauss-Bonnet gravities, Class. Quant. Grav. 27 (2010) 095007 [arXiv:1001.3636] [INSPIRE];
R. Myrzakulov, D. S aez-G omez and A. Tureanu, On the CDM Universe in f(G) gravity, Gen. Rel. Grav. 43 (2011) 1671 [arXiv:1009.0902] [INSPIRE];
A. de la Cruz-Dombriz and D. Sáez-Gómez, On the stability of the cosmological solutions in f(R;G) gravity, Class. Quant. Grav. 29 (2012) 245014 [arXiv:1112.4481] [INSPIRE].
[5] C. Brans and R. Dicke, Mach's principle and a relativistic theory of gravitation, Phys. Rev. 124 (1961) 925 [INSPIRE];
C. Brans, Mach's Principle and a Relativistic Theory of Gravitation. II, Phys. Rev. 125 (1962)2194 [INSPIRE];
J. García-Bellido, A.D. Linde and D.A. Linde, Fluctuations of the gravitational constant in the inflationary Brans-Dicke cosmology, Phys. Rev. D 50 (1994) 730 [astro-ph/9312039] [INSPIRE];
J.A. Cembranos, K.A. Olive, M. Peloso and J.-P. Uzan, Quantum Corrections to the Cosmological Evolution of Conformally Coupled Fields, JCAP 07 (2009) 025 [arXiv:0905.1989] [INSPIRE];
T. Biswas, J.A. Cembranos and J.I. Kapusta, Thermal Duality and Hagedorn Transition from
pradic Strings, Phys. Rev. Lett. 104 (2010) 021601 [arXiv:0910.2274] [INSPIRE];
T. Biswas, J.A. Cembranos and J.I. Kapusta, Thermodynamics and Cosmological Constant of
Non-Local Field Theories from p-Adic Strings, JHEP 10 (2010) 048 [arXiv:1005.0430] [INSPIRE];
T. Biswas, J.A. Cembranos and J.I. Kapusta, Finite Temperature Solitons in Non-Local Field
Theories from p-Adic Strings, Phys. Rev. D 82 (2010) 085028 [arXiv:1006.4098] [INSPIRE].
[6] L. Ford, Inflation driven by a vector eld, Phys. Rev. D 40 (1989) 967 [INSPIRE];
J. Beltrán Jiménez and A.L. Maroto, A cosmic vector for dark energy, Phys. Rev. D 78 (2008) 063005;
J. Beltrán Jiménez and A.L. Maroto, Cosmological electromagnetic elds and dark energy, JCAP 03 (2009) 016 [arXiv:0811.0566] [INSPIRE];
J. Beltran Jimenez and A.L. Maroto, Cosmological evolution in vector-tensor theories of gravity, Phys. Rev. D 80 (2009) 063512 [arXiv:0905.1245] [INSPIRE];
T. Koivisto and D.F. Mota, Vector Field Models of Inflation and Dark Energy, JCAP 08 (2008) 021 [arXiv:0805.4229] [INSPIRE];
J. Cembranos, C. Hallabrin, A. Maroto and S.N. Jareno, Isotropy theorem for cosmological vector fields, Phys. Rev. D 86 (2012) 021301 [arXiv:1203.6221] [INSPIRE];
J. Cembranos, A. Maroto and S.N. Jareno, Isotropy theorem for cosmological Yang-Mills theories, Phys. Rev. D 87 (2013) 043523 [arXiv:1212.3201] [INSPIRE].
[7] J. Alcaraz, J. Cembranos, A. Dobado and A.L. Maroto, Limits on the brane uctuations mass and on the brane tension scale from electron positron colliders, Phys. Rev. D 67 (2003) 075010 [hep-ph/0212269] [INSPIRE];
L3 collaboration, P. Achard et al., Search for branons at LEP, Phys. Lett. B 597 (2004) 145 [hep-ex/0407017] [INSPIRE];
J. Cembranos, A. Dobado and A.L. Maroto, Brane world dark matter, Phys. Rev. Lett. 90 (2003) 241301 [hep-ph/0302041] [INSPIRE];
J. Cembranos, A. Dobado and A.L. Maroto, Cosmological and astrophysical limits on brane fluctuations, Phys. Rev. D 68 (2003) 103505 [hep-ph/0307062] [INSPIRE];
J. Cembranos, A. Dobado and A.L. Maroto, Phenomenological implications of brane world scenarios with low tension, AIP Conf. Proc. 670 (2003) 235 [hep-ph/0301009] [INSPIRE];
J. Cembranos, A. Dobado and A.L. Maroto, Dark geometry, Int. J. Mod. Phys. D 13 (2004) 2275 [hep-ph/0405165] [INSPIRE];
J. Cembranos, A. Dobado and A.L. Maroto, Branon search in hadronic colliders, Phys. Rev. D 70 (2004) 096001 [hep-ph/0405286] [INSPIRE];
J. Cembranos, A. Dobado and A.L. Maroto, Branon radiative corrections to collider physics and precision observables, Phys. Rev. D 73 (2006) 035008 [hep-ph/0510399] [INSPIRE];
J. Cembranos, A. Dobado and A.L. Maroto, Dark matter clues in the muon anomalous magnetic moment, Phys. Rev. D 73 (2006) 057303 [hep-ph/0507066] [INSPIRE];
J. Cembranos, A. Dobado and A.L. Maroto, Some model-independent phenomenological consequences of exible brane worlds, J. Phys. A 40 (2007) 6631 [hep-ph/0611024] [INSPIRE].
[8] D.Z. Freedman, P. van Nieuwenhuizen and S. Ferrara, Progress Toward a Theory of Supergravity, Phys. Rev. D 13 (1976) 3214 [INSPIRE];
S. Deser and B. Zumino, Consistent Supergravity, Phys. Lett. B 62 (1976) 335 [INSPIRE];
E. Cremmer, B. Julia and J. Scherk, Supergravity Theory in Eleven-Dimensions, Phys. Lett. B
76 (1978) 409 [INSPIRE];
L.J. Hall, J.D. Lykken and S. Weinberg, Supergravity as the Messenger of Supersymmetry Breaking, Phys. Rev. D 27 (1983) 2359 [INSPIRE];
N. Ohta, Grand uni ed theories based on local supersymmetry, Prog. Theor. Phys. 70 (1983) 542 [INSPIRE];
L. Álvarez-Gaumé, J. Polchinski and M.B. Wise, Minimal Low-Energy Supergravity, Nucl. Phys. B 221 (1983) 495 [INSPIRE];
H.P. Nilles, Supersymmetry, Supergravity and Particle Physics, Phys. Rept. 110 (1984) 1 [INSPIRE];
J.A. Cembranos, J.L. Feng, A. Rajaraman and F. Takayama, SuperWIMP solutions to small scale structure problems, Phys. Rev. Lett. 95 (2005) 181301 [hep-ph/0507150] [INSPIRE];
J. Cembranos, J.L. Feng, A. Rajaraman and F. Takayama, Gravitino and axino superWIMPs, AIP Conf. Proc. 903 (2007) 591 [hep-ph/0701011] [INSPIRE];
J.A. Cembranos, J.L. Feng and L.E. Strigari, Resolving Cosmic Gamma Ray Anomalies with Dark Matter Decaying Now, Phys. Rev. Lett. 99 (2007) 191301 [arXiv:0704.1658] [INSPIRE];
J.A. Cembranos, J.L. Feng and L.E. Strigari, Exotic Collider Signals from the Complete Phase Diagram of Minimal Universal Extra Dimensions, Phys. Rev. D 75 (2007) 036004 [hep-ph/0612157] [INSPIRE];
M.R. Garousi, Ricci curvature corrections to type-II supergravity, Phys. Rev. D 87 (2013) 025006 [arXiv:1210.4379] [INSPIRE].
[9] G.W. Horndeski, Second-order scalar-tensor eld equations in a four-dimensional space, Int. J.
Theor. Phys. 10 (1974) 363 [INSPIRE];
J.D. Bekenstein, The Relation between physical and gravitational geometry, Phys. Rev. D 48 (1993) 3641 [gr-qc/9211017] [INSPIRE];
J. Cembranos, A. Dobado and A.L. Maroto, Brane skyrmions and wrapped states, Phys. Rev. D 65 (2002) 026005 [hep-ph/0106322] [INSPIRE];
J. Cembranos, A. de la Cruz-Dombriz, A. Dobado and A.L. Maroto, Is the CMB Cold Spot a gate to extra dimensions?, JCAP 10 (2008) 039 [arXiv:0803.0694] [INSPIRE];
J. Cembranos, A. de la Cruz-Dombriz, A. Dobado, R. Lineros and A. Maroto, Photon spectra from WIMP annihilation, Phys. Rev. D 83 (2011) 083507 [arXiv:1009.4936] [INSPIRE];
J.A. Cembranos, J.L. Diaz-Cruz and L. Prado, Impact of DM direct searches and the LHC analyses on branon phenomenology, Phys. Rev. D 84 (2011) 083522 [arXiv:1110.0542] [INSPIRE];
J. Cembranos, A. de la Cruz-Dombriz, V. Gammaldi and A. Maroto, Detection of branon dark matter with gamma ray telescopes, Phys. Rev. D 85 (2012) 043505 [arXiv:1111.4448] [INSPIRE];
J. Cembranos, V. Gammaldi and A. Maroto, Possible dark matter origin of the gamma ray emission from the galactic center observed by HESS, Phys. Rev. D 86 (2012) 103506 [arXiv:1204.0655] [INSPIRE];
J.A. Cembranos and L.E. Strigari, Diffuse MeV Gamma-rays and Galactic 511 keV Line from Decaying WIMP Dark Matter, Phys. Rev. D 77 (2008) 123519 [arXiv:0801.0630] [INSPIRE];
M. Zumalacarregui, T. Koivisto, D. Mota and P. Ruiz-Lapuente, Disformal Scalar Fields and the Dark Sector of the Universe, JCAP 05 (2010) 038 [arXiv:1004.2684] [INSPIRE];
T.S. Koivisto, D.F. Mota and M. Zumalacarregui, Screening Modications of Gravity through Disformally Coupled Fields, Phys. Rev. Lett. 109 (2012) 241102 [arXiv:1205.3167] [INSPIRE];
M. Zumalacarregui, T.S. Koivisto and D.F. Mota, DBI Galileons in the Einstein Frame: Local Gravity and Cosmology, Phys. Rev. D 87 (2013) 083010 [arXiv:1210.8016] [INSPIRE].
[10] V.A. Kostelecky and S. Samuel, Spontaneous Breaking of Lorentz Symmetry in String Theory, Phys. Rev. D 39 (1989) 683 [INSPIRE];
D. Colladay and V.A. Kostelecky, CPT violation and the standard model, Phys. Rev. D 55 (1997) 6760 [hep-ph/9703464] [INSPIRE];
J.R. Ellis, N. Mavromatos and D.V. Nanopoulos, A microscopic recoil model for light cone uctuations in quantum gravity, Phys. Rev. D 61 (2000) 027503 [gr-qc/9906029] [INSPIRE];
J. Alfaro, H.A. Morales-Tecotl and L.F. Urrutia, Quantum gravity corrections to neutrino propagation, Phys. Rev. Lett. 84 (2000) 2318 [gr-qc/9909079] [INSPIRE];
G. Amelino-Camelia, Doubly special relativity, Nature 418 (2002) 34 [gr-qc/0207049] [INSPIRE];
J. Magueijo and L. Smolin, Lorentz invariance with an invariant energy scale, Phys. Rev. Lett. 88 (2002) 190403 [hep-th/0112090] [INSPIRE];
J. Cembranos, A. Rajaraman and F. Takayama, CPT violation in the top sector, hep-ph/0512020 [INSPIRE];
J. Cembranos, A. Rajaraman and F. Takayama, Searching for CPT violation in tt production, Europhys. Lett. 82 (2008) 21001 [hep-ph/0609244] [INSPIRE];
S. Ghosh and P. Pal, Deformed Special Relativity and Deformed Symmetries in a Canonical Framework, Phys. Rev. D 75 (2007) 105021 [hep-th/0702159] [INSPIRE].
[11] T.P. Sotiriou, 6 + 1 lessons from f(R) gravity, J. Phys. Conf. Ser. 189 (2009) 012039 [arXiv:0810.5594] [INSPIRE];
S. Capozziello and M. De Laurentis, Extended Theories of Gravity, Phys. Rept. 509 (2011) 167 [arXiv:1108.6266] [INSPIRE];
S. Nojiri and S.D. Odintsov, Uni ed cosmic history in modi ed gravity: from F(R) theory to Lorentz non-invariant models, Phys. Rept. 505 (2011) 59 [arXiv:1011.0544] [INSPIRE]; T.P. Sotiriou and V. Faraoni, f(R) theories of gravity, Rev. Mod. Phys. 82 (2010) 451 [arXiv:0805.1726] [INSPIRE];
A. de la Cruz-Dombriz and D. S aez-G omez, Black holes, cosmological solutions, future singularities, and their thermodynamical properties in modi ed gravity theories, Entropy 14 (2012) 1717.
[12] T.P. Sotiriou, The Nearly Newtonian regime in non-linear theories of gravity, Gen. Rel. Grav. 38 (2006) 1407 [gr-qc/0507027] [INSPIRE];
S. Nojiri and S.D. Odintsov, Uni ed cosmic history in modi ed gravity: from F(R) theory to Lorentz non-invariant models, Phys. Rept. 505 (2011) 59 [arXiv:1011.0544] [INSPIRE];
B. Jain and J. Khoury, Cosmological Tests of Gravity, Annals Phys. 325 (2010) 1479 [arXiv:1004.3294] [INSPIRE];
A. de la Cruz-Dombriz, A. Dobado and A.L. Maroto, On the evolution of density perturbations in f(R) theories of gravity, Phys. Rev. D 77 (2008) 123515 [arXiv:0802.2999] [INSPIRE];
A. de la Cruz-Dombriz, A. Dobado and A. Maroto, Comment on \Viable singularity-free f(R) gravity without a cosmological constant", Phys. Rev. Lett. 103 (2009) 179001 [arXiv:0910.1441] [INSPIRE];
M. Abdelwahab, A. Abebe, A. de la Cruz Dombriz and P.K.S. Dunsby, Covariant gauge-invariant perturbations in multifluid f(R) gravity, Class. Quant. Grav. 29 (2012) 135011 [arXiv:1110.1191];
J. Cembranos, A. de la Cruz-Dombriz and B. Montes N u~nez, Gravitational collapse in f(R) theories, JCAP 04 (2012) 021 [arXiv:1201.1289] [INSPIRE];
B. Montes N u~nez, J. Cembranos and A. de la Cruz-Dombriz, On the collapse in fourth order gravities, AIP Conf. Proc. 1458 (2011) 491 [arXiv:1210.7968] [INSPIRE];
H. Bourhrous, A. de la Cruz-Dombriz and P. Dunsby, CMB Tensor Anisotropies in Metric f(R) Gravity, AIP Conf. Proc. 1458 (2011) 343 [arXiv:1202.3862] [INSPIRE];
A. Abebe, A. de la Cruz-Dombriz and P.K.S. Dunsby, Large Scale Structure Constraints for a Class of f(R) Theories of Gravity, arXiv:1304.3462 [INSPIRE];
F. Alvarenga, A. de la Cruz-Dombriz, M. Houndjo, M. Rodrigues and D. S aez-G omez, Dynamics of scalar perturbations in f(R; T) gravity, Phys. Rev. D 87 (2013) 103526 [arXiv:1302.1866] [INSPIRE].
[13] S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press, Cambridge U.K. (1973).
[14] R.M. Wald, General Relativity, University of Chicago Press, Chicago U.S.A. (1984).
[15] A. Raychaudhuri, Relativistic cosmology. 1, Phys. Rev. 98 (1955) 1123 [INSPIRE].
[16] R. Sachs, Gravitational waves in general relativity. 6. The outgoing radiation condition, Proc. Roy. Soc. Lond. A 264 (1961) 309 [INSPIRE].
[17] J. Ehlers, Contributions to the relativistic mechanics of continuous media, Gen. Rel. Grav. 25 (1993) 1225, English translation of original German article by P. Jordan, J. Ehlers, W. Kundt and R.K. Sachs, [Abh. Akad. Wiss. Lit. Mainz. Nat. Kl. 11 (1961) 792] [INSPIRE].
[18] G.F.R. Ellis, On the Raychaudhuri equation, Pramana 69 (2007) 15; S. Kar and S. SenGupta, The Raychaudhuri equations: A Brief review, Pramana 69 (2007) 49 [gr-qc/0611123] [INSPIRE];
N. Dadhich, Derivation of the Raychaudhuri equation, gr-qc/0511123 [INSPIRE].
[19] F. Albareti, J. Cembranos and A. de la Cruz-Dombriz, Focusing of geodesic congruences in an accelerated expanding Universe, JCAP 12 (2012) 020 [arXiv:1208.4201] [INSPIRE].
[20] L.P. Eisenhart, Riemannian Geometry, Princeton University Press, Princeton U.S.A. (1926).
[21] J. Santos, J. Alcaniz, M. Reboucas and F. Carvalho, Energy conditions in f(R)-gravity, Phys. Rev. D 76 (2007) 083513 [arXiv:0708.0411] [INSPIRE];
J. Santos, M. Reboucas and J. Alcaniz, Energy conditions constraints on a class of f(R)-gravity, Int. J. Mod. Phys. D 19 (2010) 1315 [arXiv:0807.2443] [INSPIRE].
[22] K. Atazadeh, A. Khaleghi, H. Sepangi and Y. Tavakoli, Energy conditions in f(R) gravity and Brans-Dicke theories, Int. J. Mod. Phys. D 18 (2009) 1101 [arXiv:0811.4269] [INSPIRE].
[23] O. Bertolami and M.C. Sequeira, Energy Conditions and Stability in f(R) theories of gravity with non-minimal coupling to matter, Phys. Rev. D 79 (2009) 104010 [arXiv:0903.4540] [INSPIRE].
[24] N.M. Garcia, T. Harko, F.S. Lobo and J.P. Mimoso, Energy conditions in modified Gauss-Bonnet gravity, Phys. Rev. D 83 (2011) 104032 [arXiv:1011.4159] [INSPIRE];
N. Montelongo Garcia, F.S. Lobo, J.P. Mimoso and T. Harko, f(G) modi ed gravity and the energy conditions, J. Phys. Conf. Ser. 314 (2011) 012056 [arXiv:1012.0953] [INSPIRE].
[25] A. Banijamali, B. Fazlpour and M. Setare, Energy Conditions in f(G) Modi�ed Gravity with Non-minimal Coupling to Matter, Astrophys. Space Sci. 338 (2012) 327 [arXiv:1111.3878] [INSPIRE].
[26] Y.-Y. Zhao et al., Modied f(G) gravity models with curvature-matter coupling, Eur. Phys. J. C 72 (2012) 1924 [arXiv:1203.5593] [INSPIRE].
[27] A. de la Cruz-Dombriz and A. Dobado, A f(R) gravity without cosmological constant, Phys. Rev. D 74 (2006) 087501 [gr-qc/0607118] [INSPIRE];
P.K. Dunsby, E. Elizalde, R. Goswami, S. Odintsov and D.S. Gomez, On the LCDM Universe in f(R) gravity, Phys. Rev. D 82 (2010) 023519 [arXiv:1005.2205] [INSPIRE];
S. Nojiri and S.D. Odintsov, Modi ed f(R) gravity consistent with realistic cosmology: From matter dominated epoch to dark energy universe, Phys. Rev. D 74 (2006) 086005 [hep-th/0608008] [INSPIRE].
[28] A. Dolgov and M. Kawasaki, Can modi ed gravity explain accelerated cosmic expansion?, Phys. Lett. B 573 (2003) 1 [astro-ph/0307285] [INSPIRE].
[29] T. Clifton, P.G. Ferreira, A. Padilla and C. Skordis, Modied Gravity and Cosmology, Phys. Rept. 513 (2012) 1 [arXiv:1106.2476] [INSPIRE].
[30] S. Capozziello and S. Vignolo, The Cauchy problem for f(R)-gravity: An Overview, Int. J. Geom. Meth. Mod. Phys. 9 (2012) 1250006 [arXiv:1103.2302] [INSPIRE].
[31] L. Pogosian and A. Silvestri, The pattern of growth in viable f(R) cosmologies, Phys. Rev. D 77 (2008) 023503 [Erratum ibid. D 81 (2010) 049901] [arXiv:0709.0296] INSPIRE].
[32] J. Cembranos, The Newtonian limit at intermediate energies, Phys. Rev. D 73 (2006) 64029 [gr-qc/0507039] [INSPIRE].
[33] B. Jain, V. Vikram and J. Sakstein, Astrophysical Tests of Modi ed Gravity: Constraints from Distance Indicators in the Nearby Universe, arXiv:1204.6044 [INSPIRE];
L. Lombriser, A. Slosar, U. Seljak and W. Hu, Constraints on f(R) gravity from probing the large-scale structure, Phys. Rev. D 85 (2012) 124038 [arXiv:1003.3009] [INSPIRE];
L. Lombriser et al., Cluster Density Profiles as a Test of Modi ed Gravity, Phys. Rev. D 85 (2012) 102001 [arXiv:1111.2020] [INSPIRE];
Y.-S. Song, H. Peiris and W. Hu, Cosmological Constraints on f(R) Acceleration Models, Phys. Rev. D 76 (2007) 063517 [arXiv:0706.2399] [INSPIRE].
[34] Y.-S. Song, W. Hu and I. Sawicki, The Large Scale Structure of f(R) Gravity, Phys. Rev. D 75 (2007) 044004 [astro-ph/0610532] [INSPIRE].
[35] R. Bousso, The Holographic principle, Rev. Mod. Phys. 74 (2002) 825 [hep-th/0203101] [INSPIRE].
[36] S.M. Carroll, V. Duvvuri, M. Trodden and M.S. Turner, Is cosmic speed - up due to new gravitational physics?, Phys. Rev. D 70 (2004) 043528 [astro-ph/0306438] [INSPIRE].
[37] V. Faraoni, Matter instability in modified gravity, Phys. Rev. D 74 (2006) 104017 [astro-ph/0610734] [INSPIRE].
[38] A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
[39] J.A. Cembranos, Dark Matter from R2-gravity, Phys. Rev. Lett. 102 (2009) 141301 [arXiv:0809.1653] [INSPIRE].
[40] C.P. Berry and J.R. Gair, Linearized f(R) gravity: gravitational radiation and solar system tests, Phys. Rev. D 83 (2011) 104022 [Erratum ibid. D 85 (2012) 089906] [arXiv:1104.0819] [INSPIRE].
[41] A.L. Erickcek, T.L. Smith and M. Kamionkowski, Solar System tests do rule out 1=R gravity, Phys. Rev. D 74 (2006) 121501 [astro-ph/0610483] [INSPIRE];
M. Fairbairn and S. Rydbeck, Expansion history and f(R) modified gravity, JCAP 12 (2007) 005 [astro-ph/0701900] [INSPIRE];
I. Sawicki and W. Hu, Stability of Cosmological Solution in f(R) Models of Gravity, Phys. Rev. D 75 (2007) 127502 [astro-ph/0702278] [INSPIRE].
[42] L. Amendola, R. Gannouji, D. Polarski and S. Tsujikawa, Conditions for the cosmological viability of f(R) dark energy models, Phys. Rev. D 75 (2007) 083504 [gr-qc/0612180] [INSPIRE].
[43] A. de la Cruz-Dombriz, A. Dobado and A. Maroto, Black Holes in f(R) theories, Phys. Rev. D 80 (2009) 124011 [Erratum ibid. D 83 (2011) 029903] [arXiv:0907.3872] [INSPIRE];
J. Cembranos, A. de la Cruz-Dombriz and P.J. Romero, Kerr-Newman black holes in f(R) theories, arXiv:1109.4519 [INSPIRE];
P. Jimeno Romero, J. Cembranos and A. de la Cruz-Dombriz, Modified spinning black holes, AIP Conf. Proc. 1458 (2011) 439 [arXiv:1202.0853] [INSPIRE].
[44] W. Hu and I. Sawicki, Models of f(R) Cosmic Acceleration that Evade Solar-System Tests, Phys. Rev. D 76 (2007) 064004 [arXiv:0705.1158] [INSPIRE].
[45] V. Faraoni, Solar System experiments do not yet veto modified gravity models, Phys. Rev. 74 (2006) 023529 [gr-qc/0607016] [INSPIRE];
I. Navarro and K. Van Acoleyen, Consistent long distance modification of gravity from inverse powers of the curvature, JCAP 03 (2006) 008 [gr-qc/0511045] [INSPIRE];
G. Calcagni, B. de Carlos and A. De Felice, Ghost conditions for Gauss-Bonnet cosmologies, Nucl. Phys. B 752 (2006) 404 [hep-th/0604201] [INSPIRE];
G.J. Olmo, Post-Newtonian constraints on f(R) cosmologies in metric and Palatini formalism, Phys. Rev. D 72 (2005) 083505 [gr-qc/0505135] [INSPIRE];
G.J. Olmo, The Gravity Lagrangian according to solar system experiments, Phys. Rev. Lett. 95 (2005) 261102 [gr-qc/0505101] [INSPIRE];
S. Capozziello, V. Cardone and A. Troisi, Low surface brightness galaxies rotation curves in the low energy limit of Rn gravity: no need for dark matter?, Mon. Not. Roy. Astron. Soc. 375 (2007) 1423 [astro-ph/0603522] [INSPIRE].
[46] C.P. Berry and J.R. Gair, Linearized f(R) Gravity: Gravitational Radiation and Solar System Tests, Phys. Rev. D 83 (2011) 104022 [Erratum ibid. D 85 (2012) 089906] [arXiv:1104.0819] [INSPIRE].
[47] F.D. Albareti, J.A.R. Cembranos, A. de la Cruz-Dombriz and A. Dobado, The Focusing Theorem and Raychaudhuri equation in f(R) gravity theories, in progress.