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Models of vacuum energy interacting with cold dark matter: Constraints and comparison

Abstract

In this paper, we investigate the observational constraints on the scenario of vacuum energy interacting with cold dark matter. We consider eight typical interaction forms in such an interacting vacuum energy scenario. The observational data used in this work to constrain these models include the JLA sample of type Ia supernovae observation, the Planck 2015 distance priors data of cosmic microwave background anisotropies observation, the baryon acoustic oscillations data, and the Hubble constant direct measurement. We find that the current observational data almost equally favor these interacting vacuum energy models. We also find that for all these models of vacuum energy interacting with cold dark matter the case of no interaction is actually well consistent with the current observational data within 1σ range.

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References

  1. 1.

    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, 1009 (1998).

  2. 2.

    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, 565 (1999), arXiv: astro-ph/9812133.

  3. 3.

    D. N. Spergel, L. Verde, H. V. Peiris, E. Komatsu, M. R. Nolta, C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page, G. S. Tucker, J. L. Weiland, E. Wollack, and E. L. Wright, Astrophy. J. Suppl. S. 148, 175 (2003), arXiv: astroph/0302209.

  4. 4.

    C. L. Bennett, M. Halpern, G. Hinshaw, N. Jarosik, A. Kogut, M. Limon, S. S. Meyer, L. Page, D. N. Spergel, G. S. Tucker, E. Wollack, E. L. Wright, C. Barnes, M. R. Greason, R. S. Hill, E. Komatsu, M. R. Nolta, N. Odegard, H. V. Peiris, L. Verde, and J. L. Weiland, Astrophy. J. Suppl. S. 148, 1 (2003), arXiv: astro-ph/0302207.

  5. 5.

    M. Tegmark, et al. (SDSS Collaboration), Phys. Rev. D 69, 103501 (2004), arXiv: astro-ph/0310723.

  6. 6.

    K. Abazajian, et al. (SDSS Collaboration), Astron. J. 128, 502 (2004), arXiv: astro-ph/0403325.

  7. 7.

    V. Sahni, and A. Starobinsky, Int. J. Mod. Phys. D 15, 2105 (2006).

  8. 8.

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

  9. 9.

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

  10. 10.

    P. J. E. Peebles, and B. Ratra, Rev. Mod. Phys. 75, 559 (2003).

  11. 11.

    E. J. Copeland, M. Sami, and S. Tsujikawa, Int. J. Mod. Phys. D 15, 1753 (2006), arXiv: hep-th/0603057.

  12. 12.

    J. A. Frieman, M. S. Turner, and D. Huterer, Annu. Rev. Astron. Astrophys. 46, 385 (2008), arXiv: 0803.0982.

  13. 13.

    V. Sahni, Prog. Theor. Phys. Suppl. 172, 110 (2008).

  14. 14.

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

  15. 15.

    M. Kamionkowski, arXiv: 0706.2986.

  16. 16.

    P. A. R. Ade, et al. (Planck Collaboration), Astron. Astrophys. 594, A13 (2016), arXiv: 1502.01589.

  17. 17.

    V. Sahni, and A. Starobinsky, Int. J. Mod. Phys. D 09, 373 (2000).

  18. 18.

    R. Bean, S. M. Carroll, and M. Trodden, arXiv: astro-ph/0510059.

  19. 19.

    L. Amendola, Phys. Rev. D 62, 043511 (2000), arXiv: astroph/9908023.

  20. 20.

    L. Amendola, Phys. Rev. D 60, 043501 (1999), arXiv: astroph/9904120.

  21. 21.

    D. Tocchini-Valentini, and L. Amendola, Phys. Rev. D 65, 063508 (2002).

  22. 22.

    L. Amendola, and D. Tocchini-Valentini, Phys. Rev. D 66, 043528 (2002).

  23. 23.

    D. Comelli, M. Pietroni, and A. Riotto, Phys. Lett. B 571, 115 (2003).

  24. 24.

    L. P. Chimento, A. S. Jakubi, D. Pavón, and W. Zimdahl, Phys. Rev. D 67, 083513 (2003).

  25. 25.

    R. G. Cai, and A. Wang, J. Cosmol. Astropart. Phys. 2005, 2 (2005).

  26. 26.

    X. Zhang, F. Q. Wu, and J. Zhang, J. Cosmol. Astropart. Phys. 2006, 3 (2006).

  27. 27.

    F. Ferrer, S. Räsänen, and J. Väliviita, J. Cosmol. Astropart. Phys. 2004, 10 (2004).

  28. 28.

    W. Zimdahl, Int. J. Mod. Phys. D 14, 2319 (2005).

  29. 29.

    X. Zhang, Phys. Lett. B 611, 1 (2005).

  30. 30.

    B. Wang, J. Zang, C. Y. Lin, E. Abdalla, and S. Micheletti, Nucl. Phys. B 778, 69 (2007).

  31. 31.

    H. M. Sadjadi, and M. Alimohammadi, Phys. Rev. D 74, 103007 (2006).

  32. 32.

    J. D. Barrow, and T. Clifton, Phys. Rev. D 73, 103520 (2006).

  33. 33.

    M. Sasaki, J. Väliviita, and D. Wands, Phys. Rev. D 74, 103003 (2006).

  34. 34.

    E. Abdalla, L. R. Abramo, L. Sodré Jr., and B. Wang, Phys. Lett. B 673, 107 (2009), arXiv: 0710.1198.

  35. 35.

    R. Bean, É. É. Flanagan, and M. Trodden, Phys. Rev. D 78, 023009 (2008), arXiv: 0709.1128.

  36. 36.

    Z. K. Guo, N. Ohta, and S. Tsujikawa, Phys. Rev. D 76, 023508 (2007).

  37. 37.

    O. Bertolami, F. Gil Pedro, and M. Le Delliou, Phys. Lett. B 654, 165 (2007).

  38. 38.

    C. G. Böhmer, G. Caldera-Cabral, R. Lazkoz, and R. Maartens, Phys. Rev. D 78, 023505 (2008), arXiv: 0801.1565.

  39. 39.

    J. H. He, and B. Wang, J. Cosmol. Astropart. Phys. 2008, 10 (2008), arXiv: 0801.4233.

  40. 40.

    G. Caldera-Cabral, R. Maartens, and L. A. Urena-López, Phys. Rev. D 79, 063518 (2009), arXiv: 0812.1827.

  41. 41.

    R. Bean, 1. Flanagan, I. Laszlo, and M. Trodden, Phys. Rev. D 78, 123514 (2008), arXiv: 0808.1105.

  42. 42.

    M. Szydlowski, A. Krawiec, A. Kurek, and M. Kamionka, Eur. Phys. J. C 75, 5 (2015), arXiv: 0801.0638.

  43. 43.

    X. Chen, Y. Gong, and E. N. Saridakis, J. Cosmol. Astropart. Phys. 2009, 1 (2009), arXiv: 0812.1117.

  44. 44.

    J. Väliviita, E. Majerotto, and R. Maartens, J. Cosmol. Astropart. Phys. 2008, 20 (2008), arXiv: 0804.0232.

  45. 45.

    E. Couderc, and S. Klein, Phys. Rev. Lett. 103, 062504 (2009), arXiv: 0901.1161.

  46. 46.

    L. P. Chimento, Phys. Rev. D 81, 043525 (2010), arXiv: 0911.5687.

  47. 47.

    G. Caldera-Cabral, R. Maartens, and B. M. Schaefer, J. Cosmol. Astropart. Phys. 2009, 27 (2009), arXiv: 0905.0492.

  48. 48.

    E. Majerotto, J. Väliviita, and R. Maartens, Mon. Not. R. Astron. Soc. 402, 2344 (2010), arXiv: 0907.4981.

  49. 49.

    J. Väliviita, R. Maartens, and E. Majerotto, Mon. Not. R. Astron. Soc. 402, 2355 (2010), arXiv: 0907.4987.

  50. 50.

    J. H. He, B. Wang, and Y. P. Jing, J. Cosmol. Astropart. Phys. 2009, 30 (2009), arXiv: 0902.0660.

  51. 51.

    J. H. He, B. Wang, and P. Zhang, Phys. Rev. D 80, 063530 (2009), arXiv: 0906.0677.

  52. 52.

    K. Koyama, R. Maartens, and Y. S. Song, J. Cosmol. Astropart. Phys. 2009, 17 (2009), arXiv: 0907.2126.

  53. 53.

    M. Li, X. D. Li, S. Wang, Y. Wang, and X. Zhang, J. Cosmol. Astropart. Phys. 2009, 14 (2009), arXiv: 0910.3855.

  54. 54.

    J. Q. Xia, Phys. Rev. D 80, 103514 (2009), arXiv: 0911.4820.

  55. 55.

    R. G. Cai, and Q. Su, Phys. Rev. D 81, 103514 (2010), arXiv: 0912.1943.

  56. 56.

    J. H. He, B. Wang, E. Abdalla, and D. Pavon, J. Cosmol. Astropart. Phys. 2010, 22 (2010), arXiv: 1001.0079.

  57. 57.

    J. Cui, and X. Zhang, Phys. Lett. B 690, 233 (2010), arXiv: 1005.3587.

  58. 58.

    B. Li, and J. D. Barrow, Mon. Not. R. Astron. Soc. 413, 262 (2011), arXiv: 1010.3748.

  59. 59.

    M. B. Gavela, L. L. Honorez, O. Mena, and S. Rigolin, J. Cosmol. Astropart. Phys. 2010, 44 (2010), arXiv: 1005.0295.

  60. 60.

    M. Martinelli, L. L. Honorez, A. Melchiorri, and O. Mena, Phys. Rev. D 81, 103534 (2010), arXiv: 1004.2410.

  61. 61.

    J. H. He, B. Wang, and E. Abdalla, Phys. Rev. D 83, 063515 (2011), arXiv: 1012.3904.

  62. 62.

    Y. Chen, Z. H. Zhu, L. Xu, and J. S. Alcaniz, Phys. Lett. B 698, 175 (2011), arXiv: 1103.2512.

  63. 63.

    T. F. Fu, J. F. Zhang, J. Q. Chen, and X. Zhang, Eur. Phys. J. C 72, 1932 (2012), arXiv: 1112.2350.

  64. 64.

    T. Clemson, K. Koyama, G. B. Zhao, R. Maartens, and J. Väliviita, Phys. Rev. D 85, 043007 (2012), arXiv: 1109.6234.

  65. 65.

    Y. H. Li, and X. Zhang, Eur. Phys. J. C 71, 1700 (2011), arXiv: 1103.3185.

  66. 66.

    X. D. Xu, J. H. He, and B. Wang, Phys. Lett. B 701, 513 (2011), arXiv: 1103.2632.

  67. 67.

    Z. Zhang, S. Li, X. D. Li, X. Zhang, and M. Li, J. Cosmol. Astropart. Phys. 2012, 9 (2012), arXiv: 1204.6135.

  68. 68.

    X. D. Xu, B. Wang, P. Zhang, and F. Atrio-Barandela, J. Cosmol. Astropart. Phys. 2013, 1 (2013), arXiv: 1308.1475.

  69. 69.

    M. J. Zhang, and W. B. Liu, Eur. Phys. J. C 74, 2863 (2014), arXiv: 1312.0224.

  70. 70.

    Y. Wang, D. Wands, L. Xu, J. De-Santiago, and A. Hojjati, Phys. Rev. D 87, 083503 (2013), arXiv: 1301.5315.

  71. 71.

    V. Salvatelli, A. Marchini, L. Lopez-Honorez, and O. Mena, Phys. Rev. D 88, 023531 (2013), arXiv: 1304.7119.

  72. 72.

    W. Yang, and L. Xu, Phys. Rev. D 89, 083517 (2014), arXiv: 1401.1286.

  73. 73.

    W. Yang, and L. Xu, J. Cosmol. Astropart. Phys. 2014, 34 (2014), arXiv: 1401.5177.

  74. 74.

    S. Wang, Y. Z. Wang, J. J. Geng, and X. Zhang, Eur. Phys. J. C 74, 3148 (2014), arXiv: 1406.0072.

  75. 75.

    V. Faraoni, J. B. Dent, and E. N. Saridakis, Phys. Rev. D 90, 063510 (2014), arXiv: 1405.7288.

  76. 76.

    J. L. Cui, L. Yin, L. F. Wang, Y. H. Li, and X. Zhang, J. Cosmol. Astropart. Phys. 2015, 24 (2015), arXiv: 1503.08948.

  77. 77.

    Y. Fan, P. Wu, and H. Yu, Phys. Lett. B 746, 230 (2015).

  78. 78.

    T. Yang, Z. K. Guo, and R. G. Cai, Phys. Rev. D 91, 123533 (2015), arXiv: 1505.04443.

  79. 79.

    D. G. A. Duniya, D. Bertacca, and R. Maartens, Phys. Rev. D 91, 063530 (2015), arXiv: 1502.06424.

  80. 80.

    L. Feng, and X. Zhang, J. Cosmol. Astropart. Phys. 2016, 72 (2016), arXiv: 1607.05567.

  81. 81.

    R. Murgia, S. Gariazzo, and N. Fornengo, J. Cosmol. Astropart. Phys. 2016, 14 (2016), arXiv: 1602.01765.

  82. 82.

    J. Solá, A. Gómez-Valent, and J. C. Pérez, Astrophys. J. 836, 43 (2017), arXiv: 1602.02103.

  83. 83.

    J. Solá Peracaula, J. de Cruz Pérez, and A. Gómez-Valent, Eurphys. Lett. 121, 39001 (2018).

  84. 84.

    J. Solá, Int. J. Mod. Phys. A 31, 1630035 (2016), arXiv: 1612.02449.

  85. 85.

    A. Pourtsidou, and T. Tram, Phys. Rev. D 94, 043518 (2016), arXiv: 1604.04222.

  86. 86.

    A. A. Costa, X. D. Xu, B. Wang, and E. Abdalla, J. Cosmol. Astropart. Phys. 2017, 28 (2017), arXiv: 1605.04138.

  87. 87.

    D. M. Xia, and S. Wang, Mon. Not. R. Astron. Soc. 463, 952 (2016), arXiv: 1608.04545.

  88. 88.

    C. van de Bruck, J. Mifsud, and J. Morrice, Phys. Rev. D 95, 043513 (2017), arXiv: 1609.09855.

  89. 89.

    S. Kumar, and R. C. Nunes, Phys. Rev. D 94, 123511 (2016), arXiv: 1608.02454.

  90. 90.

    S. Kumar, and R. C. Nunes, Phys. Rev. D 96, 103511 (2017), arXiv: 1702.02143.

  91. 91.

    L. Santos, W. Zhao, E. G. M. Ferreira, and J. Quintin, Phys. Rev. D 96, 103529 (2017), arXiv: 1707.06827.

  92. 92.

    J. Solá Peracaula, J. de Cruz Pérez, and A. Gómez-Valent, Mon. Not. R. Astron. Soc. 478, 4357 (2018), arXiv: 1703.08218.

  93. 93.

    R. Y. Guo, Y. H. Li, J. F. Zhang, and X. Zhang, J. Cosmol. Astropart. Phys. 2017, 40 (2017), arXiv: 1702.04189.

  94. 94.

    X. Zhang, Sci. China-Phys. Mech. Astron. 60, 050431 (2017), arXiv: 1702.04564.

  95. 95.

    L. Feng, Y. H. Li, F. Yu, J. F. Zhang, and X. Zhang, Eur. Phys. J. C 78, 865 (2018), arXiv: 1807.03022.

  96. 96.

    R. Y. Guo, J. F. Zhang, and X. Zhang, J. Cosmol. Astropart. Phys. 2019, 54 (2019), arXiv: 1809.02340.

  97. 97.

    M. M. Zhao, R. Y. Guo, J. F. Zhang, and X. Zhang, arXiv: 1810.11658.

  98. 98.

    L. Feng, H. L. Li, J. F. Zhang, and X. Zhang, arXiv: 1903.08848.

  99. 99.

    W. Yang, S. Pan, E. D. Valentino, R. C. Nunes, S. Vagnozzi, and D. F. Mota, J. Cosmol. Astropart. Phys. 2018, 19 (2018), arXiv: 1805.08252.

  100. 100.

    C. Li, X. Ren, M. Khurshudyan and Y. F. Cai, arXiv: 1904.02458.

  101. 101.

    Y. H. Li, J. F. Zhang, and X. Zhang, Phys. Rev. D 93, 023002 (2016), arXiv: 1506.06349.

  102. 102.

    J. J. Guo, J. F. Zhang, Y. H. Li, D. Z. He, and X. Zhang, Sci. China-Phys. Mech. Astron. 61, 030011 (2018), arXiv: 1710.03068.

  103. 103.

    R. Y. Guo, J. F. Zhang, and X. Zhang, Chin. Phys. C 42, 095103 (2018), arXiv: 1803.06910.

  104. 104.

    L. Feng, J. F. Zhang, and X. Zhang, Phys. Dark Univ. 23, 100261 (2019), arXiv: 1712.03148.

  105. 105.

    X. Zhang, Mod. Phys. Lett. A 20, 2575 (2005).

  106. 106.

    J. Zhang, X. Zhang, and H. Liu, Phys. Lett. B 659, 26 (2008), arXiv: 0705.4145.

  107. 107.

    L. Zhang, J. Cui, J. Zhang, and X. Zhang, Int. J. Mod. Phys. D 19, 21 (2010), arXiv: 0911.2838.

  108. 108.

    Y. H. Li, J. Z. Ma, J. L. Cui, Z. Wang, and X. Zhang, Sci. China-Phys. Mech. Astron. 54, 1367 (2011), arXiv: 1011.6122.

  109. 109.

    Y. H. Li, J. F. Zhang, and X. Zhang, Phys. Rev. D 90, 063005 (2014), arXiv: 1404.5220.

  110. 110.

    Y. H. Li, J. F. Zhang, and X. Zhang, Phys. Rev. D 90, 123007 (2014), arXiv: 1409.7205.

  111. 111.

    J. F. Zhang, L. A. Zhao, and X. Zhang, Sci. China-Phys. Mech. Astron. 57, 387 (2014), arXiv: 1306.1289.

  112. 112.

    Y. H. Li, and X. Zhang, Phys. Rev. D 89, 083009 (2014), arXiv: 1312.6328.

  113. 113.

    J. J. Geng, Y. H. Li, J. F. Zhang, and X. Zhang, Eur. Phys. J. C 75, 356 (2015), arXiv: 1501.03874.

  114. 114.

    A. P. Billyard, and A. A. Coley, Phys. Rev. D 61, 083503 (2000).

  115. 115.

    H. L. Li, J. F. Zhang, L. Feng, and X. Zhang, Eur. Phys. J. C 77, 907 (2017), arXiv: 1711.06159.

  116. 116.

    D. Pavón, and B. Wang, Gen. Relativ. Gravit. 41, 1 (2009), arXiv: 0712.0565.

  117. 117.

    L. Amendola, G. C. Campos, and R. Rosenfeld, Phys. Rev. D 75, 083506 (2007).

  118. 118.

    S. del Campo, R. Herrera, and D. Pavón, Phys. Rev. D 71, 123529 (2005).

  119. 119.

    G. Olivares, F. Atrio-Barandela, and D. Pavón, Phys. Rev. D 71, 063523 (2005).

  120. 120.

    B. Wang, Y. Gong, and E. Abdalla, Phys. Lett. B 624, 141 (2005).

  121. 121.

    H. Akaike, IEEE Trans. Automat. Contr. 19, 716 (1974).

  122. 122.

    G. Schwarz, Ann. Statist. 6, 461 (1978).

  123. 123.

    P. A. R. Ade, et al. (Planck Collaboration), Astron. Astrophys. 594, A14 (2016), arXiv: 1502.01590.

  124. 124.

    F. Beutler, C. Blake, M. Colless, D. H. Jones, L. Staveley-Smith, L. Campbell, Q. Parker, W. Saunders, and F. Watson, Mon. Not. R. Astron. Soc. 416, 3017 (2011), arXiv: 1106.3366.

  125. 125.

    A. J. Ross, L. Samushia, C. Howlett, W. J. Percival, A. Burden, and M. Manera, Mon. Not. R. Astron. Soc. 449, 835 (2015), arXiv: 1409.3242.

  126. 126.

    L. Anderson, 1. Aubourg, S. Bailey, F. Beutler, V. Bhardwaj, M. Blanton, A. S. Bolton, J. Brinkmann, J. R. Brownstein, A. Burden, C. H. Chuang, A. J. Cuesta, K. S. Dawson, D. J. Eisenstein, S. Escoffier, J. E. Gunn, H. Guo, S. Ho, K. Honscheid, C. Howlett, D. Kirkby, R. H. Lupton, M. Manera, C. Maraston, C. K. McBride, O. Mena, F. Montesano, R. C. Nichol, S. E. Nuza, M. D. Olmstead, N. Padmanabhan, N. Palanque-Delabrouille, J. Parejko, W. J. Percival, P. Petitjean, F. Prada, A. M. Price-Whelan, B. Reid, N. A. Roe, A. J. Ross, N. P. Ross, C. G. Sabiu, S. Saito, L. Samushia, A. G. Sánchez, D. J. Schlegel, D. P. Schneider, C. G. Scoccola, H. J. Seo, R. A. Skibba, M. A. Strauss, M. E. C. Swanson, D. Thomas, J. L. Tinker, R. Tojeiro, M. V. Magaña, L. Verde, D. A. Wake, B. A. Weaver, D. H. Weinberg, M. White, X. Xu, C. Yéche, I. Zehavi, and G. B. Zhao, Mon. Not. R. Astron. Soc. 441, 24 (2014), arXiv: 1312.4877.

  127. 127.

    G. Efstathiou, Mon. Not. R. Astron. Soc. 440, 1138 (2014), arXiv: 1311.3461.

  128. 128.

    A. G. Riess, L. Macri, S. Casertano, H. Lampeitl, H. C. Ferguson, A. V. Filippenko, S. W. Jha, W. Li, and R. Chornock, Astrophys. J. 730, 119 (2011), arXiv: 1103.2976; Astrophys. J. 732, 129 (2011).

  129. 129.

    G. B. Zhao, J. Q. Xia, M. Li, B. Feng, and X. Zhang, Phys. Rev. D 72, 123515 (2005).

  130. 130.

    J. H. He, B. Wang, and E. Abdalla, Phys. Lett. B 671, 139 (2009), arXiv: 0807.3471.

  131. 131.

    H. Gil-Marín, W. J. Percival, L. Verde, J. R. Brownstein, C. H. Chuang, F. S. Kitaura, S. A. Rodríguez-Torres, and M. D. Olmstead, Mon. Not. R. Astron. Soc. 465, 1757 (2017), arXiv: 1606.00439.

  132. 132.

    M. Betoule, R. Kessler, J. Guy, J. Mosher, D. Hardin, R. Biswas, P. Astier, P. El-Hage, M. Konig, S. Kuhlmann, J. Marriner, R. Pain, N. Regnault, C. Balland, B. A. Bassett, P. J. Brown, H. Campbell, R. G. Carlberg, F. Cellier-Holzem, D. Cinabro, A. Conley, C. B. D’Andrea, D. L. DePoy, M. Doi, R. S. Ellis, S. Fabbro, A. V. Filippenko, R. J. Foley, J. A. Frieman, D. Fouchez, L. Galbany, A. Goobar, R. R. Gupta, G. J. Hill, R. Hlozek, C. J. Hogan, I. M. Hook, D. A. Howell, S. W. Jha, L. Le Guillou, G. Leloudas, C. Lidman, J. L. Marshall, A. Möller, A. M. Mourão, J. Neveu, R. Nichol, M. D. Olmstead, N. Palanque-Delabrouille, S. Perlmutter, J. L. Prieto, C. J. Pritchet, M. Richmond, A. G. Riess, V. Ruhlmann-Kleider, M. Sako, K. Schahmaneche, D. P. Schneider, M. Smith, J. Sollerman, M. Sullivan, N. A. Walton, and C. J. Wheeler, Astron. Astrophys. 568, A22 (2014), arXiv: 1401.4064.

  133. 133.

    A. G. Riess, L. M. Macri, S. L. Hoffmann, D. Scolnic, S. Casertano, A. V. Filippenko, B. E. Tucker, M. J. Reid, D. O. Jones, J. M. Silverman, R. Chornock, P. Challis, W. Yuan, P. J. Brown, and R. J. Foley, Astrophys. J. 826, 56 (2016), arXiv: 1604.01424.

  134. 134.

    C. Heymans, E. Grocutt, A. Heavens, M. Kilbinger, T. D. Kitching, F. Simpson, J. Benjamin, T. Erben, H. Hildebrandt, H. Hoekstra, Y. Mellier, L. Miller, L. Van Waerbeke, M. L. Brown, J. Coupon, L. Fu, J. Harnois-Déraps, M. J. Hudson, K. Kuijken, B. Rowe, T. Schrabback, E. Semboloni, S. Vafaei, and M. Velander, Mon. Not. R. Astron. Soc. 432, 2433 (2013), arXiv: 1303.1808.

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Author information

Correspondence to Xin Zhang.

Additional information

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11875102, 11835009, 11522540, and 11690021), the National Program for Support of Top-Notch Young Professionals, and Doctoral Research Project of Shenyang Normal University (Grant Nos. BS201844, and BS201702).

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Li, H., Feng, L., Zhang, J. et al. Models of vacuum energy interacting with cold dark matter: Constraints and comparison. Sci. China Phys. Mech. Astron. 62, 120411 (2019). https://doi.org/10.1007/s11433-019-9439-8

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Keywords

  • interacting dark energy
  • interacting vacuum energy models
  • cosmological observations
  • cosmological constraints
  • model comparison