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Nonlocal Models of Cosmic Acceleration

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Abstract

I review a class of nonlocally modified gravity models which were proposed to explain the current phase of cosmic acceleration without dark energy. Among the topics considered are deriving causal and conserved field equations, adjusting the model to make it support a given expansion history, why these models do not require an elaborate screening mechanism to evade solar system tests, degrees of freedom and kinetic stability, and the negative verdict of structure formation. Although these simple models are not consistent with data on the growth of cosmic structures many of their features are likely to carry over to more complicated models which are in better agreement with the data.

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References

  1. Riess, A.G., et al.: Astron. J. 116, 1009 (1998). astro-ph/9805201

  2. Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999). astro-ph/9812133

  3. Hicken, M., et al.: Astrophys. J. 700, 1097 (2009). arXiv:0901.4804

  4. WMAP Collabration.: arXiv:1212.5226

  5. Hou, Z., et al.: arXiv:1212.6267

  6. Sievers, J.L., et al.: arXiv:1301.0802

  7. Planck Collaboration.: arXiv:1303.5076

  8. Nojiri, S.I., Odintsov, S.D.: Phys. Rep. 505, 59 (2011). arXiv:1011.0544

  9. Li, M., Li, X.-D., Wang, S., Wang, Y.: Commun. Theor. Phys. 56, 525 (2011). arXiv:1103.5870

    Google Scholar 

  10. Bamba, K., Capozziello, S., Nojiri, S.I., Odintsov, S.D.: Astrophys. Space Sci. 342, 155 (2012). arXiv:1205.3421

  11. Wang, Y., Mukherjee, P.: Astrophys. J. 650, 1 (2006). astro-ph/0604051

  12. Alam, U., Sahni, V., Starobinsky, A.A.: JCAP 0702, 011 (2007). astro-ph/0612381

  13. Wang, Y.: Dark Energy. Wiley, Weinheim (2010)

    Book  Google Scholar 

  14. Weinberg, S.: Rev. Mod. Phys. 61, 1 (1989)

    Google Scholar 

  15. Sahni, V., Starobinsky, A.: Int. J. Mod. Phys. D9, 373 (2000). astro-ph/9904398

  16. Carroll, S.M.: Living Rev. Rel. 4, 1 (2001). astro-ph/0004075

  17. Ratra, B., Peebles, P.J.E.: Rev. Mod. Phys. 75, 559 (2003). astro-ph/0207347

  18. Ratra, B., Peebles, P.J.E.: Phys. Rev. D37, 3406 (1988)

    Google Scholar 

  19. Wetterich, C.: Nucl. Phys. B302, 668 (1988)

  20. Zlatev, I., Wang, L.-M., Steinhardt, P.J.: Phys. Rev. Lett. 82, 896 (1999). astro-ph/9807002

    Google Scholar 

  21. Steinhardt, P.J., Wang, L.M., Zlatev, I.: Phys. Rev. D59, 123504 (1999). astro-ph/9812313

  22. Wang, L.-M., Caldwell, R.R., Ostriker, J.P., Steinhardt, P.J.: Astrophys. J. 530, 17 (2000). astro-ph/9901388

  23. Tsamis, N.C., Woodard, R.P.: Ann. Phys. 267, 145 (1998). hep-ph/971233

  24. Saini, T.D., Raychaudhury, S., Sahni, V., Starobinsky, A.A.: Phys. Rev. Lett. 85 (2000). astro-ph/9910231

  25. Capozziello, S., Nojiri, S., Odintsov, S.D.: Phys. Lett. B634, 93 (2006). hep-th/0512118

  26. Guo, Z.K., Ohta, N., Zhang, Y.Z.: Phys. Rev. D72, 023504 (2005). astro-ph/0505253

  27. Guo, Z.K., Ohta, N., Zhang, Y.Z.: Mod. Phys. Lett. A22, 883 (2007). astro-ph/0603109

  28. Parker, L., Raval, A.: Phys. Rev. D60, 063512 (1999). gr-qc/9905031

  29. Parker, L., Vanzella, D.A.T.: Phys. Rev. D69, 104009 (2004). gr-qc/0312108

  30. Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: Phys. Rev. D70, 043528 (2004). astro-ph/0306438

  31. Nojiri, S., Odintsov, S.D.: Int. J. Geom. Meth. Mod. Phys. 4, 115 (2007). hep-th/0601213

  32. Hu, W., Sawicki, I.: Phys. Rev. D76, 064004 (2007). arXiv:0705.1158

  33. Appleby, S.A., Battye, R.A.: Phys. Lett. B654, 7 (2007). arXiv:0705.3199

  34. Starobinsky, A.A.: JETP Lett. 86, 157 (2007). arXiv:0706.2041

  35. Woodard, R.P.: Lect. Notes Phys. 720, 403 (2007). astro-ph/0601672

  36. Dunsby, P.K.S., Elizalde, E., Goswami, R., Odintsov, S., Gomez, D.S.: Phys. Rev. D82, 023519 (2010). arXiv:1005.2205

  37. Parker, L., Toms, D.J.: Phys. Rev. D32, 1409 (1985)

  38. Banks, T.: Nucl. Phys. B309, 493 (1988)

  39. Wetterich, C.: Gen. Rel. Grav. 30, 159 (1998). gr-qc/9704052

  40. Barvinsky, A.O.: Phys. Lett. B572, 109 (2003). hep-th/0304229

  41. Espriu, D., Multamaki, T., Vagenas, E.C.: Phys. Lett. B628, 197 (2005). gr-qc/0503033

  42. Hamber, H.W., Williams, R.M.: Phys. Rev. D72, 044026 (2005). hep-th/0507017

  43. Biswas, T., Mazumdar, A., Siegel, W.: JCAP 0603, 009 (2006). hep-th/0508194

  44. Lopez Nacir, D., Mazzitelli F.D.: Phys. Rev. D75, 024003 (2007). hep-th/0610031

  45. Khoury, J.: Phys. Rev. D76, 123513 (2007). hep-th/0612052

  46. Capozziello, S., Elizalde, E., Nojiri, S.I., Odintsov, S.D.: Phys. Lett. B671, 193 (2009). arXiv:0809.1535

  47. Biswas, T., Koivisto, T., Mazumdar, A.: JCAP 1011, 008 (2010). arXiv:1005.0590

  48. Zhang, Y.-L., Sasaki, M.: Int. J. Mod. Phys. D21, 1250006 (2012). arXiv:1108.2112

  49. Barvinsky, A.O: Phys. Lett. b710, 12 (2012). arXiv:1107.1463

  50. Barvinsky, A.O.: Phys. Rev. D85, 104018 (2012). arXiv:1112.4340

  51. Elizalde, E., Pozdeeva, E.O., Vernov, S.Y.: Phys. Rev. D85, 044002 (2012). arXiv:1110.5806

  52. Barvinsky, A.O., Gusev, Y.V.: Phys. Part. Nucl. 44, 213 (2013). arXiv:1209.3062

  53. Biswas, T., Conroy, A., Koshelev, A.S., Mazumdar, A.: Class. Quant. Grav. 31, 015022 (2013). arXiv:1308.2319

  54. Ferreira, P.G., Maroto, A.L.: Phys. Rev. D88, 123502 (2013). arXiv:1310.1238

  55. Foffa, S., Maggiore, M., Mitsou, E.: arXiv:1311.3421, arXiv:1311.3435

  56. Soussa, M.E., Woodard, R.P.: Class. Quant. Grav. 20, 2737 (2003). astro-ph/0302030

  57. Deffayet, C., Esposito-Farese, G., Woodard, R.P.: Phys. Rev. D84, 124054 (2011). arXiv:1106.4984

  58. Newton, I.: in Four Letters from Sir Isaac Newton to Doctor Bentley (R. and J. Dodsley, Pall-Mall, 1756)

  59. Eliezer, D.A., Woodard, R.P.: Nucl. Phys. B325, 389 (1989)

    Google Scholar 

  60. Tsamis, N.C., Woodard, R.P.: Nucl. Phys. B474, 235 (1996). hep-ph/9602315

  61. Tsamis, N.C., Woodard, R.P.: Int. J. Mod. Phys. D20, 2847 (2011). arXiv:1103.5134

  62. Starobinsky, A.A.: JETP Lett. 30, 682 (1979)

  63. Polyakov, A.M.: Sov. Phys. Usp. 25, 187 (1982)

  64. Tsamis, N.C., Woodard, R.P.: Ann. Phys. 238, 1 (1995)

    Google Scholar 

  65. Weinberg, S.: Phys. Rev. 140, B516 (1965)

  66. Veneziano, G.: Nucl. Phys. B44, 142 (1972)

  67. Tsamis, N.C., Woodard, R.P.: Ann. Phys. 253, 1 (1997). hep-ph/9602316

  68. Starobinsky, A.A., Yokoyama, J.: Phys. Rev. D50, 6357 (1994). astro-ph/9407016

  69. Tsamis, N.C., Woodard, R.P.: Nucl. Phys. B724 (2005) 295, gr-qc/0505115

  70. Miao, S.P., Woodard, R.P.: Phys. Rev. D74, 044019 (2006). gr-qc/0602110

  71. Prokopec, T., Tsamis, N.C., Woodard, R.P.: Ann. Phys. 323, 1324 (2008). arXiv:0707.0847

  72. Miao, S.P., Woodard, R.P.: Class. Quant. Grav. 25, 145009 (2008). arXiv:0803.2377

  73. Kitamoto, H., Kitazawa, Y.: Phys. Rev. D83, 104043 (2011). arXiv:1012.5930

  74. Kitamoto, H., Kitazawa, Y.: Phys. Rev. D85, 044062 (2012). arXiv:1109.4892

  75. S. Deser and R. P. Woodard, Phys. Rev. Lett. 99 (2007) 111301, arXiv:0706.2151

  76. Bertschinger, E.: Astrophys. J. 648, 797 (2006). astro-ph/0604485

  77. Hu, W., Sawicki, I.: Phys. Rev. 76, 104043 (2007). arXiv:0708.1190

  78. Wang, Y.: JCAP 0805, 021 (2008). arXiv:0710.3885

  79. Baker, T., Perreira, P.G., Skordis, C.: Phys. Rev. D87 (2013) 024015, arXiv:1209.2117

  80. Simpson, F., et al.: arXiv:1212.3339

  81. Huterer, D., et al.: arXiv:1309.5385

  82. Koivisto, T.: Phys. Rev. D77, 123513 (2008). arXiv:0803.3399

  83. Koivisto, T.: Phys. Rev. D78, 123505 (2008). arXiv:0807.3778

  84. Park, S., Dodelson, S.: Phys. Rev. D87, 024003 (2013). arXiv:1209.0836

  85. Dodelson, S., Park, S.: arXiv:1310.4329

  86. Schwinger, J.: J. Math. Phys. 2, 407 (1961)

    Google Scholar 

  87. Mahanthappa, K.T.: Phys. Rev. 126, 329 (1962)

    Google Scholar 

  88. Bakshi, P.M., Mahanthappa, K.T.: J. Math. Phys. 4, 1 (1963)

    Google Scholar 

  89. Bakshi, P.M., Mahanthappa, K.T.: J. Math. Phys. 4, 12 (1963)

    Google Scholar 

  90. Keldysh, L.V.: Sov. Phys. JETP 20, 1018 (1965)

    Google Scholar 

  91. Chou, K.C., Su, Z.B., Hao, B.L., Yu, L.: Phys. Rep. 118, 1 (1985)

    Google Scholar 

  92. Jordan, R.D.: Phys. Rev. D33, 444 (1986)

  93. Calzetta, E., Hu, B.L.: Phys. Rev. D35, 495 (1987)

  94. Deffayet, C., Woodard, R.P.: JCAP 0908, 023 (2009). arXiv:0904.0961

  95. Elizalde, E., Pozdeeva, E.O., Yu Vernov, S.: Class. Quant. Grav. 30, 035002 (2013). arXiv:1209.5957

    Google Scholar 

  96. Elizalde, E., Pozdeeva, E.O., Yu Vernov, S., Zhang, Y.-L.: arXiv:1302.4330

  97. Dunkley, J., et al.: Astrophys. J. Suppl. 180, 306 (2009). arXiv:0803.0586

  98. Komatsu, E., et al.: Astrophys. J. Suppl. 180, 330 (2009). arXiv:0803.0547

  99. Khoury, J., Weltman, A.: Phys. Rev. Lett. 93, 171104 (2004). astro-ph/0309300

    Google Scholar 

  100. Khoury, J., Weltman, A.: Phys. Rev. D69, 044026 (2004). astro-ph/0309411

  101. Brax, P., van de Bruck, C., Davis, A.-C., Khoury, J., Weltman, A.: Phys. Rev. D70, 123518 (2004). astro-ph/0408415

  102. Deser, S., Woodard, R.P.: JCAP 1311, 036 (2013). arXiv:1307.6639

  103. Nojiri, S.I., Odintsov, S.D.: Phys. Lett. B659, 821 (2008). arXiv:0708.0924

  104. Koshelev, N.A.: Grav. Cosmol. 15, 220 (2009). arXiv:0809.4927

  105. Nojiri, S.I., Odintsov, S.D., Sasaki, M., Zhang, Y.-I.: Phys. Lett. B696, 278 (2011). arXiv:1010.5375

  106. Lifshitz, E.M.: J. Phys. USSR 10, 116 (1946)

    Google Scholar 

  107. Tsamis, N.C., Woodard, R.P.: Phys. Rev. D82, 063502 (2010). arXiv:1006.4834

  108. Tsamis, N.C., Woodard, R.P.: Phys. Rev. D80, 083512 (2009). arXiv:0904.2368

  109. Romania, M.G., Tsamis, N.C., Woodard, R.P.: Lect. Notes Phys.863, 375 (2013). arXiv:1204.6558

    Google Scholar 

  110. Tsamis, N.C., Woodard, R.P.: Phys. Rev. D81, 103509 (2010). arXiv:1001.4929

  111. Milgrom, M.: Astrophys. J. 270(365), 371 (1983)

    Google Scholar 

  112. Sanders, R.H., McGaugh, S.S.: Ann. Rev. Astron. Astrophys. 40, 263 (2002). astro-ph/0204521

    Google Scholar 

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Acknowledgments

It is a pleasure to thank my distinguished colleagues and collaborators: C. Deffayet, S. Deser, S. Dodelson, G. Esposito-Farese, S. Park and N. C. Tsamis. This work was partiallysupported by NSF Grant PHY-1205591.

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Woodard, R.P. Nonlocal Models of Cosmic Acceleration. Found Phys 44, 213–233 (2014). https://doi.org/10.1007/s10701-014-9780-6

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