Curing singularities in cosmological evolution of F(R) gravity

Journal of Cosmology and Astroparticle Physics

Volumn 2010, Issue 6, 2010, Pages

  Appleby, Stephen A ^a   Battye, Richard A ^a   Starobinsky, Alexei A ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b LANDAU INSTITUTE FOR THEORETICAL PHYSICS   (Russian Federation)

Author keywords

dark energy theory; inflation; modified gravity

Indexed keywords

EID: 77954036218     PISSN: 14757516     EISSN: 14757516     Source Type: Journal    
DOI: 10.1088/1475-7516/2010/06/005     Document Type: Article

References (80)

1. V. Sahni and A.A. Starobinsky, 2000 The case for a positive cosmological Λ-term, Int. J. Mod. Phys. D 9 373 [astro-ph/9904398]
2. T. Padmanabhan, 2003 Cosmological constant: the weight of the vacuum, Phys. Rept. 380 235 [hep-th/0212290]
3. E.J. Copeland, M. Sami and S. Tsujikawa, 2006 Dynamics of dark energy, Int. J. Mod. Phys. D 15 1753 [hep-th/0603057]
4. V. Sahni and A. Starobinsky, 2006 Reconstructing dark energy, Int. J. Mod. Phys. D 15 2105 [astro-ph/0610026]
5. J. Frieman, M. Turner and D. Huterer, 2008 Dark energy and the accelerating universe, Ann. Rev. Astron. Astrophys. 46 385 [0803.0982]
6. WMAP collaboration, E. Komatsu et al., 2009 Five-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological interpretation, Astrophys. J. Suppl. 180 330 [0803.0547]
7. T.P. Sotiriou and V. Faraoni, F(R) theories of gravity, [0805.1726]
8. A.A. Starobinsky, 1980 A new type of isotropic cosmological models without singularity, Phys. Lett. B 91 99
9. V. Müller, H.-J. Schmidt and A.A. Starobinsky, 1988 The stability of the de Sitter space-time in fourth order gravity, Phys. Lett. B 202 198
10. H. Nariai, 1973 Gravitational instability of regular model-universes in a modified theory of general relativity, Prog. Theor. Phys. 49 165
11. V.T. Gurovich and A.A. Starobinsky, 1979 Quantum effects and regular cosmological models Sov. Phys. JETP 50 844
12. V.T. Gurovich and A.A. Starobinsky, 1979 Zh. Eksp. Teor. Fiz. 77 1683
13. T.V. Ruzmaikina and A.A. Ruzmaikin, 1970 Quadratic corrections to the Lagrangian gravitational field density and singularity Sov. Phys. JETP 30 372
14. T.V. Ruzmaikina and A.A. Ruzmaikin, 1970 Zh. Eksp. Teor. Fiz. 57 680
15. A.D. Dolgov and M. Kawasaki, 2003 Can modified gravity explain accelerated cosmic expansion?, Phys. Lett. B 573 1 [astro-ph/0307285]
16. L. Amendola, D. Polarski and S. Tsujikawa, 2007 Are F(R) dark energy models cosmologically viable ?, Phys. Rev. Lett. 98 131302 [astro-ph/0603703]
17. L. Amendola, R. Gannouji, D. Polarski and S. Tsujikawa, 2007 Conditions for the cosmological viability of F(R) dark energy models, Phys. Rev. D 75 083504 [gr-qc/0612180]
18. R. Utiyama and B.S. DeWitt, 1962 Renormalization of a classical gravitational field interacting with quantized matter fields, J. Math. Phys. 3 608
19. K.S. Stelle, 1977 Renormalization of higher derivative quantum gravity, Phys. Rev. D 16 953
20. J.M. Cline, S. Jeon and G.D. Moore, 2004 The phantom menaced: constraints on low-energy effective ghosts, Phys. Rev. D 70 043543 [hep-ph/0311312]
21. R. Gannouji, D. Polarski, A. Ranquet and A.A. Starobinsky, 2006 Scalar-tensor models of normal and phantom dark energy J. Cosmol. Astropart. Phys. JCAP09(2006)016 [astro-ph/0606287]
22. A. De Felice and T. Suyama, 2009 Vacuum structure for scalar cosmological perturbations in modified gravity models J. Cosmol. Astropart. Phys. JCAP06(2009)034 [0904.2092]
23. A. De Felice, D.F. Mota and S. Tsujikawa, 2010 Matter instabilities in general Gauss-Bonnet gravity, Phys. Rev. D 81 023532 [0911.1811]
24. S. Gottlöber, H.J. Schmidt and A.A. Starobinsky, 1990 Sixth order gravity and conformal transformations, Class. Quant. Grav. 7 893
25. A. Hindawi, B.A. Ovrut and D. Waldram, 1996 Non-trivial vacua in higher-derivative gravitation, Phys. Rev. D 53 5597 [hep-th/9509147]
26. N. Deruelle, M. Sasaki and Y. Sendouda, 2008 'Detuned' F(R) gravity and dark energy, Phys. Rev. D 77 124024 [0803.2742]
27. F.L. Bezrukov and M. Shaposhnikov, 2008 The standard model Higgs boson as the inflaton, Phys. Lett. B 659 703 [0710.3755]
28. F.R. Klinkhamer and G.E. Volovik, 2008 F(R) cosmology from q-theory, JETP Lett. 88 289 [0807.3896]
29. nd seminar ''Quantum gravity", Moscow Russia October 13-15 1981, INR Press, Moscow Russia, pg. 58, reprinted in Quantum gravity, M.A. Markov and P.C. West eds., Plenum Publishing Co., New York U.S.A. 1984, pg. 103 [http://www-spires.dur.ac.uk/cgi-bin/spiface/hep/www?key=1300806]
30. A. Vilenkin, 1985 Classical and quantum cosmology of the Starobinsky inflationary model, Phys. Rev. D 32 2511
31. 2 cosmology: inflation without a phase transition, Phys. Rev. D 34 2934
32. 2 cosmology, Phys. Rev. D 39 1496
33. T. Faulkner, M. Tegmark, E.F. Bunn and Y. Mao, 2007 Constraining F(R) gravity as a scalar tensor theory, Phys. Rev. D 76 063505 [astro-ph/0612569]
34. V.F. Mukhanov and G.V. Chibisov, 1981 Quantum fluctuation and nonsingular universe (in Russian), JETP Lett. 33 532
35. V.F. Mukhanov and G.V. Chibisov, 1981 Pisma Zh. Eksp. Teor. Fiz. 33 549
36. A.A. Starobinskii, 1983 The perturbation spectrum evolving from a nonsingular initially de Sitter cosmology and the microwave background anisotropy Sov. Astron. Lett. 9 302
37. A.A. Starobinsky, 1981 Evolution of small excitation of isotropic cosmological models with one loop quantum gravitation corrections (in Russian), Zh. Eksp. Teor. Fiz. 34 460
38. A.A. Starobinsky, 1981 JETP Lett. 34 438
39. L.A. Kofman, V.F. Mukhanov and D.Y. Pogosyan, 1987 The evolution of inhomogeneities in inflationary models in the theory of gravitation with higher derivatives Sov. Phys. JETP 66 433
40. L.A. Kofman, V.F. Mukhanov and D.Y. Pogosyan, 1987 Zh. Eksp. Teor. Fiz. 93 769
41. J.-C. Hwang and H. Noh, 2001 F(R) gravity theory and CMBR constraints, Phys. Lett. B 506 13 [astro-ph/0102423]
42. 2 gravity, Phys. Rev. D 30 2257
43. S. Capozziello, 2002 Curvature quintessence, Int. J. Mod. Phys. D 11 483 [gr-qc/0201033]
44. S. Capozziello, S. Carloni and A. Troisi, 2003 Quintessence without scalar fields Recent Res. Dev. Astron. Astrophys. 1 625 [astro-ph/0303041]
45. S.M. Carroll, V. Duvvuri, M. Trodden and M.S. Turner, 2004 Is cosmic speed-up due to new gravitational physics?, Phys. Rev. D 70 043528 [astro-ph/0306438]
46. S. Nojiri and S.D. Odintsov, 2003 Modified gravity with negative and positive powers of the curvature: unification of the inflation and of the cosmic acceleration, Phys. Rev. D 68 123512 [hep-th/0307288]
47. W. Hu and I. Sawicki, 2007 Models of F(R) cosmic acceleration that evade solar-system tests, Phys. Rev. D 76 064004 [0705.1158]
48. S.A. Appleby and R.A. Battye, 2007 Do consistent F(R) models mimic general relativity plus Λ?, Phys. Lett. B 654 7 [0705.3199]
49. A.A. Starobinsky, 2007 Disappearing cosmological constant in F(R) gravity, JETP Lett. 86 157 [0706.2041]
50. S. Tsujikawa, 2008 Observational signatures of F(R) dark energy models that satisfy cosmological and local gravity constraints, Phys. Rev. D 77 023507 [0709.1391]
51. S.A. Appleby and R.A. Battye, 2008 Aspects of cosmological expansion in F(R) gravity models J. Cosmol. Astropart. Phys. JCAP05(2008)019 [0803.1081]
52. A.V. Frolov, 2008 A singularity problem with F(R) dark energy, Phys. Rev. Lett. 101 061103 [0803.2500]
53. J.D. Barrow, 2004 Sudden future singularities, Class. Quant. Grav. 21 L79 [gr-qc/0403084]
54. A.O. Barvinsky, C. Deffayet and A.Y. Kamenshchik, 2008 Anomaly driven cosmology: big boost scenario and AdS/CFT correspondence J. Cosmol. Astropart. Phys. JCAP05(2008)020 [0801.2063]
55. L. Fernndez-Jambrina and R. Lazkoz, 2004 Geodesic behaviour of sudden future singularities, Phys. Rev. D 70 121503 [gr-qc/0410124]
56. J.D. Barrow, A.B. Batista, J.C. Fabris and S. Houndjo, 2008 Quantum particle production at sudden singularities, Phys. Rev. D 78 123508 [0807.4253]
57. Y.B. Zeldovich and A.A. Starobinsky, 1972 Particle production and vacuum polarization in an anisotropic gravitational field Sov. Phys. JETP 34 1159
58. Y.B. Zeldovich and A.A. Starobinsky, 1971 Zh. Eksp. Teor. Fiz. 61 2161
59. G. Cognola et al., 2008 A class of viable modified F(R) gravities describing inflation and the onset of accelerated expansion, Phys. Rev. D 77 046009 [0712.4017]
60. G. Cognola, E. Elizalde, S.D. Odintsov, P. Tretyakov and S. Zerbini, 2009 Initial and final de Sitter universes from modified F(R) gravity, Phys. Rev. D 79 044001 [0810.4989]
61. R. Dick, 2004 On the Newtonian limit in gravity models with inverse powers of R, Gen. Rel. Grav. 36 217 [gr-qc/0307052]
62. A. Dev et al., 2008 Delicate F(R) gravity models with disappearing cosmological constant and observational constraints on the model parameters, Phys. Rev. D 78 083515 [0807.3445]
63. T. Kobayashi and K.-I. Maeda, 2009 Can higher curvature corrections cure the singularity problem in F(R) gravity?, Phys. Rev. D 79 024009 [0810.5664]
64. D.J. Kapner et al., 2007 Tests of the gravitational inverse-square law below the dark-energy length scale, Phys. Rev. Lett. 98 021101 [hep-ph/0611184]
65. T. Kobayashi and K.-I. Maeda, 2008 Relativistic stars in F(R) gravity and absence thereof, Phys. Rev. D 78 064019 [0807.2503]
66. E. Babichev and D. Langlois, 2009 Relativistic stars in F(R) gravity, Phys. Rev. D 80 121501 [Erratum ibid D 81 (2010) 069901] [0904.1382]
67. A. Upadhye and W. Hu, 2009 The existence of relativistic stars in F(R) gravity, Phys. Rev. D 80 064002 [0905.4055]
68. L.A. Kofman, A.D. Linde and A.A. Starobinsky, 1985 Inflationary universe generated by the combined action of a scalar field and gravitational vacuum polarization, Phys. Lett. B 157 361
69. H.-J. Schmidt, 1989 Fourth-order gravity and conformal transformations, Class. Quant. Grav. 6 557
70. V. Müller, H.J. Schmidt and A.A. Starobinsky, 1990 Power law inflation as an attractor solution for inhomogeneous cosmological models, Class. Quant. Grav. 7 1163
71. S. Capozziello, F. Occhionero and L. Amendola, 1993 The phase space view of inflation. 2: fourth order models, Int. J. Mod. Phys. D 1 615
72. A.D. Linde, 1983 Chaotic inflation, Phys. Lett. B 129 177
73. A.D. Linde, 1982 A new inflationary universe scenario: a possible solution of the horizon, flatness, homogeneity, isotropy and primordial monopole problems, Phys. Lett. B 108 389
74. A. Albrecht and P.J. Steinhardt, 1982 Cosmology for grand unified theories with radiatively induced symmetry breaking, Phys. Rev. Lett. 48 1220
75. Y.B. Zeldovich and A.A. Starobinsky, 1977 Rate of particle production in gravitational fields JETP Lett. 26 252}.
76. L.H. Ford, 1987 Gravitational particle creation and inflation, Phys. Rev. D 35 2955
77. S. Tsujikawa, 2007 Matter density perturbations and effective gravitational constant in modified gravity models of dark energy, Phys. Rev. D 76 023514 [0705.1032]
78. Y.-S. Song, H. Peiris and W. Hu, 2007 Cosmological constraints on F(R) acceleration models, Phys. Rev. D 76 063517 [0706.2399]
79. R. Gannouji, B. Moraes and D. Polarski, 2009 The growth of matter perturbations in F(R) models J. Cosmol. Astropart. Phys. JCAP02(2009)034 [0809.3374]
80. H. Motohashi, A.A. Starobinsky and J. Yokoyama, 2009 Analytic solution for matter density perturbations in a class of viable cosmological F(R) models, Int. J. Mod. Phys. D 18 1731 [0905.0730]