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Gravity beyond general relativity

Institute of Cosmology and Gravitation, University of Portsmouth, Dennis Sciama Building, Portsmouth, PO1 3FX, UK

E-mail Address: Kazuya.Koyama@port.ac.uk

https://doi.org/10.1142/S0218271818480012Cited by:28 (Source: Crossref)

This article is part of the issue:

Special Issue — Modified Gravity: Progresses and Outlook of Theories, Numerical Techniques and Observational Tests; Editors: Baojiu Li and Kazuya Koyama

Abstract

We introduce the standard model of cosmology based on general relativity and discuss its successes and problems. We then discuss motivations to consider gravitational theories beyond general relativity and summarize observational and theoretical constraints that these theories need to satisfy. A special focus is laid on screening mechanisms, which hide deviations from general relativity in the Solar System and enable large modifications to general relativity on astrophysical and cosmological scales. Finally, several modified gravity models are introduced, which satisfy the Solar System constrains as well as the constraint on the speed of gravitational waves obtained from almost simultaneous detections of gravitational waves and gamma ray bursts from a neutron star merger (GW170817/GRB 170817A).

Keywords:

PACS: 95.36.+x

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References

1. Planck Collab. (P. A. R. Ade et al.), Astron. Astrophys. 594 (2016) A13, arXiv:1502.01589. Crossref, Web of Science, Google Scholar
2. B. P. Abbott et al., Astrophys. J. Lett. 848 (2017) L13, arXiv:1710.05834 [astro-ph.HE]. Crossref, Web of Science, ADS, Google Scholar
3. Planck Collab. (P. A. R. Ade et al.), Astron. Astrophys. 571 (2014) A16, arXiv:1303.5076. Crossref, Web of Science, Google Scholar
4. A. G. Riess, A. V. Filippenko, P. Challis, A. Clocchiatti, A. Diercks, P. M. Garnavich, R. L. Gilliland, C. J. Hogan, S. Jha, R. P. Kirshner, B. Leibundgut, M. M. Phillips, D. Reiss, B. P. Schmidt, R. A. Schommer, R. C. Smith, J. Spyromilio, C. Stubbs, N. B. Suntzeff and J. Tonry, Astron. J. 116 (1998) 1009, arXiv:astro-ph/9805201. Crossref, Web of Science, ADS, Google Scholar
5. S. Perlmutter, G. Aldering, G. Goldhaber, R. A. Knop, P. Nugent, P. G. Castro, S. Deustua, S. Fabbro, A. Goobar, D. E. Groom, I. M. Hook, A. G. Kim, M. Y. Kim, J. C. Lee, N. J. Nunes, R. Pain, C. R. Pennypacker, R. Quimby, C. Lidman, R. S. Ellis, M. Irwin, R. G. McMahon, P. Ruiz-Lapuente, N. Walton, B. Schaefer, B. J. Boyle, A. V. Filippenko, T. Matheson, A. S. Fruchter, N. Panagia, H. J. M. Newberg, W. J. Couch and T. S. C. Project, Astrophys. J. 517 (1999) 565, arXiv:astro-ph/9812133. Crossref, Web of Science, ADS, Google Scholar
6. D. J. Eisenstein, I. Zehavi, D. W. Hogg, R. Scoccimarro, M. R. Blanton, R. C. Nichol, R. Scranton, H.-J. Seo, M. Tegmark, Z. Zheng, S. F. Anderson, J. Annis, N. Bahcall, J. Brinkmann, S. Burles, F. J. Castander, A. Connolly, I. Csabai, M. Doi, M. Fukugita, J. A. Frieman, K. Glazebrook, J. E. Gunn, J. S. Hendry, G. Hennessy, Z. Ivezić, S. Kent, G. R. Knapp, H. Lin, Y.-S. Loh, R. H. Lupton, B. Margon, T. A. McKay, A. Meiksin, J. A. Munn, A. Pope, M. W. Richmond, D. Schlegel, D. P. Schneider, K. Shimasaku, C. Stoughton, M. A. Strauss, M. SubbaRao, A. S. Szalay, I. Szapudi, D. L. Tucker, B. Yanny and D. G. York, Astrophys. J. 633 (2005) 560, arXiv:astro-ph/0501171. Crossref, Web of Science, ADS, Google Scholar
7. W. J. Percival, S. Cole, D. J. Eisenstein, R. C. Nichol, J. A. Peacock, A. C. Pope and A. S. Szalay, Mon. Not. R. Astron. Soc. 381 (2007) 1053, arXiv:0705.332. Crossref, Web of Science, ADS, Google Scholar
8. Planck Collab. (P. A. R. Ade et al.), Astron. Astrophys. 594 (2016) A14, arXiv:1502.01590. Crossref, Web of Science, Google Scholar
9. H. Hildebrandt, M. Viola, C. Heymans, S. Joudaki, K. Kuijken, C. Blake, T. Erben, B. Joachimi, D. Klaes, L. Miller, C. B. Morrison, R. Nakajima, G. Verdoes Kleijn, A. Amon, A. Choi, G. Covone, J. T. A. de Jong, A. Dvornik, I. Fenech Conti, A. Grado, J. Harnois-Déraps, R. Herbonnet, H. Hoekstra, F. Köhlinger, J. McFarland, A. Mead, J. Merten, N. Napolitano, J. A. Peacock, M. Radovich, P. Schneider, P. Simon, E. A. Valentijn, J. L. van den Busch, E. van Uitert and L. Van Waerbeke, Mon. Not. R. Astron. Soc. 465 (2017) 1454, arXiv:1606.05338. Crossref, Web of Science, ADS, Google Scholar
10. DES Collab. (T. M. C. Abbott, F. B. Abdalla, A. Alarcon, J. Aleksić, S. Allam, S. Allen, A. Amara, J. Annis, J. Asorey, S. Avila, D. Bacon, E. Balbinot, M. Banerji, N. Banik, W. Barkhouse, M. Baumer, E. Baxter, K. Bechtol, M. R. Becker, A. Benoit-Lévy, B. A. Benson, G. M. Bernstein, E. Bertin, J. Blazek, S. L. Bridle, D. Brooks, D. Brout, E. Buckley-Geer, D. L. Burke, M. T. Busha, D. Capozzi, A. Carnero Rosell, M. Carrasco Kind, J. Carretero, F. J. Castander, R. Cawthon, C. Chang, N. Chen, M. Childress, A. Choi, C. Conselice, R. Crittenden, M. Crocce, C. E. Cunha, C. B. D’Andrea, L. N. da Costa, R. Das, T. M. Davis, C. Davis, J. De Vicente, D. L. DePoy, J. DeRose, S. Desai, H. T. Diehl, J. P. Dietrich, S. Dodelson, P. Doel, A. Drlica-Wagner, T. F. Eifler, A. E. Elliott, F. Elsner, J. Elvin-Poole, J. Estrada, A. E. Evrard, Y. Fang, E. Fernandez, A. Ferté, D. A. Finley, B. Flaugher, P. Fosalba, O. Friedrich, J. Frieman, J. García-Bellido, M. Garcia-Fernandez, M. Gatti, E. Gaztanaga, D. W. Gerdes, T. Giannantonio, M. S. S. Gill, K. Glazebrook, D. A. Goldstein, D. Gruen, R. A. Gruendl, J. Gschwend, G. Gutierrez, S. Hamilton, W. G. Hartley, S. R. Hinton, K. Honscheid, B. Hoyle, D. Huterer, B. Jain, D. J. James, M. Jarvis, T. Jeltema, M. D. Johnson, M. W. G. Johnson, T. Kacprzak, S. Kent, A. G. Kim, A. King, D. Kirk, N. Kokron, A. Kovacs, E. Krause, C. Krawiec, A. Kremin, K. Kuehn, S. Kuhlmann, N. Kuropatkin, F. Lacasa, O. Lahav, T. S. Li, A. R. Liddle, C. Lidman, M. Lima, H. Lin, N. MacCrann, M. A. G. Maia, M. Makler, M. Manera, M. March, J. L. Marshall, P. Martini, R. G. McMahon, P. Melchior, F. Menanteau, R. Miquel, V. Miranda, D. Mudd, J. Muir, A. Möller, E. Neilsen, R. C. Nichol, B. Nord, P. Nugent, R. L. C. Ogando, A. Palmese, J. Peacock, H. V. Peiris, J. Peoples, W. J. Percival, D. Petravick, A. A. Plazas, A. Porredon, J. Prat, A. Pujol, M. M. Rau, A. Refregier, P. M. Ricker, N. Roe, R. P. Rollins, A. K. Romer, A. Roodman, R. Rosenfeld, A. J. Ross, E. Rozo, E. S. Rykoff, M. Sako, A. I. Salvador, S. Samuroff, C. Sánchez, E. Sanchez, B. Santiago, V. Scarpine, R. Schindler, D. Scolnic, L. F. Secco, S. Serrano, I. Sevilla-Noarbe, E. Sheldon, R. C. Smith, M. Smith, J. Smith, M. Soares-Santos, F. Sobreira, E. Suchyta, G. Tarle, D. Thomas, M. A. Troxel, D. L. Tucker, B. E. Tucker, S. A. Uddin, T. N. Varga, P. Vielzeuf, V. Vikram, A. K. Vivas, A. R. Walker, M. Wang, R. H. Wechsler, J. Weller, W. Wester, R. C. Wolf, B. Yanny, F. Yuan, A. Zenteno, B. Zhang, Y. Zhang and J. Zuntz), arXiv:1708.01530. Google Scholar
11. A. G. Riess, S. Casertano, W. Yuan, L. Macri, J. Anderson, J. W. Mackenty, J. B. Bowers, K. I. Clubb, A. V. Filippenko, D. O. Jones and B. E. Tucker, ArXiv:e-prints (2018), arXiv:1801.01120 [astro-ph.SR]. Google Scholar
12. B. P. Abbott et al., Nature 551 (2017) 85, arXiv:1710.05835. Crossref, Web of Science, ADS, Google Scholar
13. S. Weinberg, Rev. Mod. Phys. 61 (1989) 1. Crossref, Web of Science, ADS, Google Scholar
14. S. R. Green and R. M. Wald, Class. Quantum Grav. 31 (2014) 234003, arXiv:1407.8084 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
15. T. Buchert, M. Carfora, G. F. R. Ellis, E. W. Kolb, M. A. H. MacCallum, J. J. Ostrowski, S. Räsänen, B. F. Roukema, L. Andersson, A. A. Coley and D. L. Wiltshire, Class. Quantum Grav. 32 (2015) 215021, arXiv:1505.07800 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
16. K. Tomita, arXiv:0906.1325 [astro-ph.CO]. Google Scholar
17. T. Clifton, P. G. Ferreira, A. Padilla and C. Skordis, Puplic Health Rep. 513 (2012) 1, arXiv:1106.2476. Google Scholar
18. A. Joyce, B. Jain, J. Khoury and M. Trodden, Puplic Health Rep. 568 (2015) 1, arXiv:1407.0059. Google Scholar
19. K. Koyama, Rep. Prog. Phys. 79 (2016) 046902, arXiv:1504.04623. Crossref, Web of Science, Google Scholar
20. J. M. Weisberg, D. J. Nice and J. H. Taylor, Astrophys. J. 722 (2010) 1030, arXiv:1011.0718 [astro-ph.GA]. Crossref, Web of Science, ADS, Google Scholar
21. B. P. Abbott et al., Phys. Rev. Lett. 116 (2016) 061102, arXiv:1602.03837 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
22. B. P. Abbott et al., Phys. Rev. Lett. 119 (2017) 161101, arXiv:1710.05832 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
23. G.-B. Zhao, M. Raveri, L. Pogosian, Y. Wang, R. G. Crittenden, W. J. Handley, W. J. Percival, F. Beutler, J. Brinkmann, C.-H. Chuang, A. J. Cuesta, D. J. Eisenstein, F.-S. Kitaura, K. Koyama, B. L’Huillier, R. C. Nichol, M. M. Pieri, S. Rodriguez-Torres, A. J. Ross, G. Rossi, A. G. Sánchez, A. Shafieloo, J. L. Tinker, R. Tojeiro, J. A. Vazquez and H. Zhang, Nature Astronomy 1 (2017) 627, arXiv:1701.08165. Crossref, Web of Science, ADS, Google Scholar
24. B. Ratra and P. J. E. Peebles, Phys. Rev. D 37 (1988) 3406. Crossref, Web of Science, ADS, Google Scholar
25. E. J. Copeland, M. Sami and S. Tsujikawa, Int. J. Mod. Phys. D 15 (2006) 1753, arXiv:hep-th/0603057. Link, Web of Science, ADS, Google Scholar
26. A. Joyce, L. Lombriser and F. Schmidt, Ann. Rev. Nucl. Part. Sci. 66 (2016) 95, arXiv:1601.06133. Crossref, Web of Science, ADS, Google Scholar
27. R. Maartens and K. Koyama, Living Rev. Rel. 13 (2010) 5, arXiv:1004.3962 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
28. C. P. Burgess, ArXiv:e-prints (2013), arXiv:1309.4133 [hep-th]. Google Scholar
29. A. Padilla, ArXiv:e-prints (2015), arXiv:1502.05296 [hep-th]. Google Scholar
30. G. Dvali, G. Gabadadze and M. Porrati, Phys. Lett. B 485 (2000) 208, arXiv:hep-th/0005016. Crossref, Web of Science, ADS, Google Scholar
31. M. A. Luty, M. Porrati and R. Rattazzi, J. High Energy Phys. 9 (2003) 029, arXiv:hep-th/0303116. Crossref, Web of Science, ADS, Google Scholar
32. D. Gorbunov, K. Koyama and S. Sibiryakov, Phys. Rev. D 73 (2006) 044016, arXiv:hep-th/0512097. Crossref, Web of Science, ADS, Google Scholar
33. C. M. Will, Living Rev. Rel. 17 (2014) 4, arXiv:1403.7377 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
34. S. M. Merkowitz, Living Rev. Rel. 13 (2010) 7. Crossref, Web of Science, ADS, Google Scholar
35. R. A. Hulse and J. H. Taylor, Astrophys. J. Lett. 195 (1975) L51. Crossref, Web of Science, ADS, Google Scholar
36. G. D. Moore and A. E. Nelson, J. High Energy Phys. 9 (2001) 023, arXiv:hep-ph/0106220. Crossref, ADS, Google Scholar
37. L. Lombriser and A. Taylor, J. Cosmol. Astropart. Phys. 3 (2016) 031, arXiv:1509.08458. Crossref, Web of Science, ADS, Google Scholar
38. L. Lombriser and N. A. Lima, Phys. Lett. B 765 (2017) 382, arXiv:1602.07670. Crossref, Web of Science, ADS, Google Scholar
39. D. Bettoni, J. M. Ezquiaga, K. Hinterbichler and M. Zumalacárregui, Phys. Rev. D 95 (2017) 084029, arXiv:1608.01982 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
40. P. Creminelli and F. Vernizzi, Phys. Rev. Lett. 119 (2017) 251302, arXiv:1710.05877. Crossref, Web of Science, ADS, Google Scholar
41. J. Sakstein and B. Jain, Phys. Rev. Lett. 119 (2017) 251303, arXiv:1710.05893. Crossref, Web of Science, ADS, Google Scholar
42. J. María Ezquiaga and M. Zumalacárregui, arXiv:1710.05901. Google Scholar
43. T. Baker, E. Bellini, P. G. Ferreira, M. Lagos, J. Noller and I. Sawicki, Phys. Rev. Lett. 119 (2017) 251301, arXiv:1710.06394. Crossref, Web of Science, ADS, Google Scholar
44. F. Sbisà, Eur. J. Phys. 36 (2015) 015009, arXiv:1406.4550 [hep-th]. Crossref, Web of Science, Google Scholar
45. A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, J. High Energy Phys. 10 (2006) 014, arXiv:hep-th/0602178. Crossref, Web of Science, ADS, Google Scholar
46. C. de Rham, S. Melville, A. J. Tolley and S.-Y. Zhou, arXiv:1706.02712 [hep-th]. Google Scholar
47. R. Woodard, Avoiding Dark Energy with 1/R Modifications of Gravity, in The Invisible Universe: Dark Matter and Dark Energy, ed. L. Papantonopoulos, Lecture Notes in Physics (Springer, Verlag, Berlin), Vol. 720 (2007), p. 403, arXiv:astro-ph/0601672. Crossref, Google Scholar
48. D. Langlois and K. Noui, J. Cosmol. Astropart. Phys. 2 (2016) 034, arXiv:1510.06930 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
49. C. Wetterich, Gen. Relativ. Gravit 30 (1998) 159, arXiv:gr-qc/9704052. Crossref, Web of Science, ADS, Google Scholar
50. S. Deser and R. P. Woodard, Phys. Rev. Lett. 99 (2007) 111301, arXiv:0706.2151. Crossref, Web of Science, ADS, Google Scholar
51. M. Maggiore and M. Mancarella, Phys. Rev. D 90 (2014) 023005, arXiv:1402.0448 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
52. E. Belgacem, Y. Dirian, S. Foffa and M. Maggiore, arXiv:1712.07066 [hep-th]. Google Scholar
53. A. Emir Gümrükçüoǧlu, M. Saravani and T. P. Sotiriou, Phys. Rev. D 97 (2018) 024032, arXiv:1711.08845 [gr-qc]. Crossref, Web of Science, Google Scholar
54. J. Oost, S. Mukohyama and A. Wang, arXiv:1802.04303 [gr-qc]. Google Scholar
55. C. de Rham, Living Rev. Relativ. 17 (2014) 7, arXiv:1401.4173 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
56. J. Khoury and A. Weltman, Phys. Rev. Lett. 93 (2004) 171104, arXiv:astro-ph/0309300. Crossref, Web of Science, ADS, Google Scholar
57. J. Khoury and A. Weltman, Phys. Rev. D 69 (2004) 044026, arXiv:astro-ph/0309411. Crossref, Web of Science, ADS, Google Scholar
58. P. Brax, C. van de Bruck, A.-C. Davis and D. Shaw, Phys. Rev. D 82 (2010) 063519, arXiv:1005.3735. Crossref, Web of Science, ADS, Google Scholar
59. K. Hinterbichler and J. Khoury, Phys. Rev. Lett. 104 (2010) 231301, arXiv:1001.4525 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
60. E. Babichev, C. Deffayet and R. Ziour, Int. J. Mod. Phys.D 18 (2009) 2147, arXiv:0905.2943 [hep-th]. Link, Web of Science, ADS, Google Scholar
61. A. I. Vainshtein, Phys. Lett. B 39 (1972) 393. Crossref, Web of Science, ADS, Google Scholar
62. P. Brax, A.-C. Davis, B. Li and H. A. Winther, Phys. Rev. D 86 (2012) 044015, arXiv:1203.4812 [astro-ph.CO]. Crossref, Web of Science, ADS, Google Scholar
63. C. Burrage and J. Sakstein, arXiv:1709.09071. Google Scholar
64. F. Rondeau and B. Li, Phys. Rev. D 96 (2017) 124009, arXiv:1709.07087 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
65. L. Amendola, Phys. Rev. D 62 (2000) 043511, arXiv:astro-ph/9908023. Crossref, Web of Science, ADS, Google Scholar
66. C. Llinares and L. Pogosian, Phys. Rev. D 90 (2014) 124041, arXiv:1410.2857. Crossref, Web of Science, ADS, Google Scholar
67. G.-B. Zhao, B. Li and K. Koyama, Phys. Rev. Lett. 107 (2011) 071303, arXiv:1105.0922 [astro-ph.CO]. Crossref, Web of Science, ADS, Google Scholar
68. A. Cabré, V. Vikram, G.-B. Zhao, B. Jain and K. Koyama, J. Cosmol. Astropart. Phys. 7 (2012) 034, arXiv:1204.6046. Crossref, Web of Science, ADS, Google Scholar
69. H. Desmond, P. G. Ferreira, G. Lavaux and J. Jasche, arXiv:1802.07206. Google Scholar
70. P. Brax, A.-C. Davis and B. Li, Phys. Lett. B 715 (2012) 38, arXiv:1111.6613. Crossref, Web of Science, ADS, Google Scholar
71. W. Hu and I. Sawicki, Phys. Rev. D 76 (2007) 064004, arXiv:0705.1158. Crossref, Web of Science, ADS, Google Scholar
72. A. Barreira, P. Brax, S. Clesse, B. Li and P. Valageas, Phys. Rev. D 91 (2015) 123522, arXiv:1504.01493. Crossref, Web of Science, ADS, Google Scholar
73. V. I. Zakharov, Sov. J. Exp. Theor. Phys. Lett. 12 (1970) 312. Web of Science, ADS, Google Scholar
74. H. van Dam and M. J. G. Veltman, Nucl. Phys. B 22 (1970) 397. Crossref, Web of Science, ADS, Google Scholar
75. D. G. Boulware and S. Deser, Phys. Rev. D 6 (1972) 3368. Crossref, Web of Science, ADS, Google Scholar
76. C. de Rham, G. Gabadadze and A. J. Tolley, Phys. Rev. Lett. 106 (2011) 231101, arXiv:1011.1232 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
77. B. Li, G.-B. Zhao and K. Koyama, J. Cosmol. Astropart. Phys. 5 (2013) 023, arXiv:1303.0008 [astro-ph.CO]. Crossref, Web of Science, ADS, Google Scholar
78. A. Lue, R. Scoccimarro and G. D. Starkman, Phys. Rev. D 69 (2004) 124015, arXiv:astro-ph/0401515. Crossref, Web of Science, ADS, Google Scholar
79. G. Dvali, A. Gruzinov and M. Zaldarriaga, Phys. Rev. D 68 (2003) 024012, arXiv:hep-ph/0212069. Crossref, Web of Science, ADS, Google Scholar
80. T. Hiramatsu, W. Hu, K. Koyama and F. Schmidt, Phys. Rev. D 87 (2013) 063525, arXiv:1209.3364 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
81. P. Brax, C. Burrage and A.-C. Davis, J. Cosmol. Astropart. Phys. 9 (2011) 020, arXiv:1106.1573 [hep-ph]. Crossref, Web of Science, ADS, Google Scholar
82. A. A. Starobinsky, Phys. Lett. B 91 (1980) 99. Crossref, Web of Science, ADS, Google Scholar
83. S. Nojiri and S. D. Odintsov, arXiv:0807.0685 [hep-th]. Google Scholar
84. T. P. Sotiriou and V. Faraoni, Rev. Mod. Phys. 82 (2010) 451, arXiv:0805.1726 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
85. A. De Felice and S. Tsujikawa, Liv. Rev. Rel. 13 (2010) 3, arXiv:1002.4928 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
86. P. Brax, C. van de Bruck, A.-C. Davis and D. J. Shaw, Phys. Rev. D 78 (2008) 104021, arXiv:0806.3415. Crossref, Web of Science, ADS, Google Scholar
87. A. A. Starobinsky, Sov. J. Exp. Theor. Phys. Lett. 86 (2007) 157, arXiv:0706.2041. Crossref, Web of Science, ADS, Google Scholar
88. S. Appleby and R. Battye, Phys. Lett. B 654 (2007) 7, arXiv:0705.3199. Crossref, Web of Science, ADS, Google Scholar
89. L. Pogosian and A. Silvestri, Phys. Rev. D 77 (2008) 023503, arXiv:0709.0296. Crossref, Web of Science, ADS, Google Scholar
90. J. Wang, L. Hui and J. Khoury, Phys. Rev. Lett. 109 (2012) 241301, arXiv:1208.4612 [astro-ph.CO]. Crossref, Web of Science, ADS, Google Scholar
91. J. J. Ceron-Hurtado, J.-H. He and B. Li, Phys. Rev. D 94 (2016) 064052, arXiv:1609.00532. Crossref, Web of Science, ADS, Google Scholar
92. Y.-S. Song, W. Hu and I. Sawicki, Phys. Rev. D 75 (2007) 044004, arXiv:astro-ph/0610532. Crossref, Web of Science, ADS, Google Scholar
93. C. Deffayet, G. Dvali and G. Gabadadze, Phys. Rev. D 65 (2002) 044023, arXiv:astro-ph/0105068. Crossref, Web of Science, ADS, Google Scholar
94. A. Lue and G. Starkman, Phys. Rev. D 67 (2003) 064002, arXiv:astro-ph/0212083. Crossref, Web of Science, ADS, Google Scholar
95. K. Koyama and F. P. Silva, Phys. Rev. D 75 (2007) 084040, arXiv:hep-th/0702169. Crossref, Web of Science, ADS, Google Scholar
96. A. Nicolis and R. Rattazzi, J. High Energy Phys. 6 (2004) 059, arXiv:hep-th/0404159. Crossref, ADS, Google Scholar
97. K. Koyama, Phys. Rev. D 72 (2005) 123511, arXiv:hep-th/0503191. Crossref, Web of Science, ADS, Google Scholar
98. C. Charmousis, R. Gregory, N. Kaloper and A. Padilla, J. High Energy Phys. 10 (2006) 066, arXiv:hep-th/0604086. Crossref, ADS, Google Scholar
99. C. Deffayet, G. Dvali, G. Gabadadze and A. Vainshtein, Phys. Rev. D 65 (2002) 044026, arXiv:hep-th/0106001. Crossref, Web of Science, ADS, Google Scholar
100. F. Schmidt, Phys. Rev. D 80 (2009) 043001, arXiv:0905.0858 [astro-ph.CO]. Crossref, Web of Science, ADS, Google Scholar
101. H. Ishihara, Phys. Rev. Lett. 86 (2001) 381, arXiv:gr-qc/0007070. Crossref, Web of Science, ADS, Google Scholar
102. G. W. Horndeski, Int. J. Theor. Phys. 10 (1974) 363. Crossref, Web of Science, ADS, Google Scholar
103. A. Nicolis, R. Rattazzi and E. Trincherini, Phys. Rev. D 79 (2009) 064036, arXiv:0811.2197 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
104. C. Deffayet, G. Esposito-Farèse and A. Vikman, Phys. Rev. D 79 (2009) 084003, arXiv:0901.1314 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
105. C. Deffayet, X. Gao, D. A. Steer and G. Zahariade, Phys. Rev. D 84 (2011) 064039, arXiv:1103.3260 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
106. C. Deffayet, S. Deser and G. Esposito-Farèse, Phys. Rev. D 80 (2009) 064015, arXiv:0906.1967 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
107. T. Kobayashi, M. Yamaguchi and J. Yokoyama, Phys. Rev. Lett. 105 (2010) 231302, arXiv:1008.0603 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
108. C. Charmousis, E. J. Copeland, A. Padilla and P. M. Saffin, Phys. Rev. Lett. 108 (2012) 051101, arXiv:1106.2000 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
109. C. Deffayet and D. A. Steer, Class. Quantum Grav. 30 (2013) 214006, arXiv:1307.2450 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
110. E. Bellini and I. Sawicki, J. Cosmol. Astropart. Phys. 7 (2014) 050, arXiv:1404.3713. Crossref, Web of Science, ADS, Google Scholar
111. C. Deffayet, O. Pujolàs, I. Sawicki and A. Vikman, J. Cosmol. Astropart. Phys. 10 (2010) 026, arXiv:1008.0048 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
112. R. Kimura and K. Yamamoto, J. Cosmol. Astropart. Phys. 4 (2011) 025, arXiv:1011.2006. Crossref, Web of Science, ADS, Google Scholar
113. R. Kimura, T. Kobayashi and K. Yamamoto, Phys. Rev. D 85 (2012) 123503, arXiv:1110.3598 [astro-ph.CO]. Crossref, Web of Science, ADS, Google Scholar
114. Z. Zhai, M. Blanton, A. Slosar and J. Tinker, Astrophys. J. 850 (2017) 183, arXiv:1705.10031. Crossref, Web of Science, ADS, Google Scholar
115. H. Motohashi, K. Noui, T. Suyama, M. Yamaguchi and D. Langlois, J. Cosmol. Astropart. Phys. 7 (2016) 033, arXiv:1603.09355 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
116. R. Klein and D. Roest, J. High Energy Phys. 7 (2016) 130, arXiv:1604.01719 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
117. M. Crisostomi, R. Klein and D. Roest, J. High Energy Phys. 6 (2017) 124, arXiv:1703.01623 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
118. H. Motohashi, T. Suyama and M. Yamaguchi (2017), arXiv:1711.08125 [hep-th]. Google Scholar
119. M. Zumalacárregui and J. García-Bellido, Phys. Rev. D 89 (2014) 064046, arXiv:1308.4685 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
120. J. Gleyzes, D. Langlois, F. Piazza and F. Vernizzi, Phys. Rev. Lett. 114 (2015) 211101, arXiv:1404.6495 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
121. J. Gleyzes, D. Langlois, F. Piazza and F. Vernizzi, J. Cosmol. Astropart. Phys. 2 (2015) 018, arXiv:1408.1952. Crossref, Web of Science, ADS, Google Scholar
122. D. Langlois and K. Noui, J. Cosmol. Astropart. Phys. 7 (2016) 016, arXiv:1512.06820 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
123. M. Crisostomi, K. Koyama and G. Tasinato, J. Cosmol. Astropart. Phys. 4 (2016) 044, arXiv:1602.03119 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
124. J. Ben Achour, D. Langlois and K. Noui, Phys. Rev. D 93 (2016) 124005, arXiv:1602.08398 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
125. J. Ben Achour, M. Crisostomi, K. Koyama, D. Langlois, K. Noui and G. Tasinato, arXiv:1608.08135 [hep-th]. Google Scholar
126. C. de Rham and A. Matas, J. Cosmol. Astropart. Phys. 6 (2016) 041, arXiv:1604.08638 [hep-th]. Crossref, Web of Science, ADS, Google Scholar
127. T. Kobayashi, Y. Watanabe and D. Yamauchi, Phys. Rev. D 91 (2015) 064013, arXiv:1411.4130 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
128. D. Langlois, R. Saito, D. Yamauchi and K. Noui, arXiv:1711.07403 [gr-qc]. Google Scholar
129. M. Crisostomi and K. Koyama, Phys. Rev. D 97 (2018) 021301, arXiv:1711.06661. Crossref, Web of Science, ADS, Google Scholar
130. K. Koyama and J. Sakstein, Phys. Rev. D 91 (2015) 124066, arXiv:1502.06872. Crossref, Web of Science, ADS, Google Scholar
131. J. Beltrán Jiménez, F. Piazza and H. Velten, Phys. Rev. Lett. 116 (2016) 061101, arXiv:1507.05047 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
132. A. Dima and F. Vernizzi, ArXiv:e-prints (2017), arXiv:1712.04731 [gr-qc]. Google Scholar
133. R. Saito, D. Yamauchi, S. Mizuno, J. Gleyzes and D. Langlois, J. Cosmol. Astropart. Phys. 6 (2015) 008, arXiv:1503.01448 [gr-qc]. Crossref, Web of Science, ADS, Google Scholar
134. J. Sakstein, Phys. Rev. Lett. 115 (2015) 201101, arXiv:1510.05964. Crossref, Web of Science, ADS, Google Scholar
135. J. Sakstein, Phys. Rev. D 92 (2015) 124045, arXiv:1511.01685. Crossref, Web of Science, ADS, Google Scholar
136. M. Crisostomi and K. Koyama, arXiv:1712.06556. Google Scholar