Galaxy cluster number count data constraints on cosmological parameters

  • L. Campanelli
  • G. L. Fogli
  • T. Kahniashvili
  • A. Marrone
  • Bharat Ratra
Regular Article - Theoretical Physics

Abstract

We use data on massive galaxy clusters (M cluster>8×1014 h −1 M within a comoving radius of R cluster=1.5h −1 Mpc) in the redshift range 0.05≲z≲0.83 to place constraints, simultaneously, on the nonrelativistic matter density parameter Ω m , on the amplitude of mass fluctuations σ 8, on the index n of the power-law spectrum of the density perturbations, and on the Hubble constant H 0, as well as on the equation-of-state parameters (w 0,w a ) of a smooth dark energy component.

For the first time, we properly take into account the dependence on redshift and cosmology of the quantities related to cluster physics: the critical density contrast, the growth factor, the mass conversion factor, the virial overdensity, the virial radius and, most importantly, the cluster number count derived from the observational temperature data.

We show that, contrary to previous analyses, cluster data alone prefer low values of the amplitude of mass fluctuations, σ 8≤0.69 (1σ C.L.), and large amounts of nonrelativistic matter, Ω m ≥0.38 (1σ C.L.), in slight tension with the ΛCDM concordance cosmological model, though the results are compatible with ΛCDM at 2σ. In addition, we derive a σ 8 normalization relation, \(\sigma_{8} \varOmega_{m}^{1/3} = 0.49 \pm 0.06\) (2σ C.L.).

Combining cluster data with σ 8-independent baryon acoustic oscillation observations, cosmic microwave background data, Hubble constant measurements, Hubble parameter determination from passively evolving red galaxies, and magnitude–redshift data of type Ia supernovae, we find \(\varOmega_{m} = 0.28^{+0.03}_{-0.02}\) and \(\sigma_{8} = 0.73^{+0.03}_{-0.03}\), the former in agreement and the latter being slightly lower than the corresponding values in the concordance cosmological model. We also find \(H_{0} = 69.1^{+1.3}_{-1.5}~\mbox {km}/\mbox {s}/\mbox {Mpc}\), the fit to the data being almost independent on n in the adopted range [0.90,1.05].

Concerning the dark energy equation-of-state parameters, we show that the present data on massive clusters weakly constrain (w 0,w a ) around the values corresponding to a cosmological constant, i.e. (w 0,w a )=(−1,0). The global analysis gives \(w_{0} = -1.14^{+0.14}_{-0.16}\) and \(w_{a} = 0.85^{+0.42}_{-0.60}\) (1σ C.L. errors). Very similar results are found in the case of time-evolving dark energy with a constant equation-of-state parameter w=const (the XCDM parametrization). Finally, we show that the impact of bounds on (w 0,w a ) is to favor top-down phantom models of evolving dark energy.

Notes

Acknowledgements

We would like to thank A. Natarajan for useful comments. T.K. acknowledges partial support from Georgian National Science Foundation grant ST08/4-422, Swiss National Science Foundation SCOPES grant 128040, NASA grant NNXlOAC85G, NSF grant AST-1109180, the ICTP associate membership program, and the Università Degli Studi Di Bari for hospitality. B.R. acknowledges support from DOE grant DEFG03-99EP41093 and NSF grant AST-1109275.

References

  1. 1.
    S.W. Allen, A.E. Evrard, A.B. Mantz, arXiv:1103.4829 [astro-ph.CO]
  2. 2.
    P.J.E. Peebles, Astrophys. J. 284, 439 (1984) ADSCrossRefGoogle Scholar
  3. 3.
    S. Weinberg, Cosmology (Oxford University Press, New York, 2008) MATHGoogle Scholar
  4. 4.
    G.M. Voit, Rev. Mod. Phys. 77, 207 (2005). arXiv:astro-ph/0410173 ADSCrossRefGoogle Scholar
  5. 5.
    P. Brax, arXiv:0912.3610 [astro-ph.CO]
  6. 6.
    J.-P. Uzan, arXiv:0912.5452 [gr-qc]
  7. 7.
    A. De Felice, S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010). arXiv:1002.4928 [gr-qc] ADSGoogle Scholar
  8. 8.
    E.V. Linder, arXiv:1004.4646 [astro-ph.CO]
  9. 9.
    A. Blanchard, Astron. Astrophys. Rev. 18, 595 (2010). arXiv:1005.3765 [astro-ph.CO] ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    D. Sapone, Int. J. Mod. Phys. A 25, 5253 (2010). arXiv:1006.5694 [astro-ph.CO] ADSMATHCrossRefGoogle Scholar
  11. 11.
    H.K. Jassal, J.S. Bagla, T. Padmanabhan, Mon. Not. R. Astron. Soc. 405, 2639 (2010). arXiv:astro-ph/0601389 ADSGoogle Scholar
  12. 12.
    K.M. Wilson, G. Chen, B. Ratra, Mod. Phys. Lett. A 21, 2197 (2006). arXiv:astro-ph/0602321 ADSCrossRefGoogle Scholar
  13. 13.
    T.M. Davis et al., Astrophys. J. 666, 716 (2007). arXiv:astro-ph/0701510 ADSCrossRefGoogle Scholar
  14. 14.
    P.J.E. Peebles, B. Ratra, Rev. Mod. Phys. 75, 559 (2003). arXiv:astro-ph/0207347 ADSMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    L. Perivolaropoulos, J. Phys. Conf. Ser. 222, 012024 (2010). arXiv:1002.3030 [astro-ph.CO] ADSCrossRefGoogle Scholar
  16. 16.
    P.J.E. Peebles, B. Ratra, Astrophys. J. Lett. 325, L17 (1988) ADSCrossRefGoogle Scholar
  17. 17.
    B. Ratra, P.J.E. Peebles, Phys. Rev. D 37, 3406 (1988) ADSCrossRefGoogle Scholar
  18. 18.
    A. Mantz, S.W. Allen, H. Ebeling, D. Rapetti, Mon. Not. R. Astron. Soc. 387, 1179 (2008). arXiv:0709.4294 [astro-ph] ADSCrossRefGoogle Scholar
  19. 19.
    A. Mantz, S.W. Allen, D. Rapetti, H. Ebeling, Mon. Not. R. Astron. Soc. 406, 1759 (2010). arXiv:0909.3098 [astro-ph.CO] ADSGoogle Scholar
  20. 20.
    A. Vikhlinin et al., Astrophys. J. 692, 1060 (2009). arXiv:0812.2720 [astro-ph] ADSCrossRefGoogle Scholar
  21. 21.
    N.A. Arhipova, T. Kahniashvili, V.N. Lukash, Astron. Astrophys. 386, 775 (2002). arXiv:astro-ph/0110426 ADSMATHCrossRefGoogle Scholar
  22. 22.
    T. Kahniashvili, E. von Toerne, N.A. Arhipova, B. Ratra, Phys. Rev. D 71, 125009 (2005). arXiv:astro-ph/0503328 ADSCrossRefGoogle Scholar
  23. 23.
    E. Rozo et al., Astrophys. J. 708, 645 (2010). arXiv:0902.3702 [astro-ph.CO] ADSCrossRefGoogle Scholar
  24. 24.
    S. Basilakos, M. Plionis, J.A.S. Lima, Phys. Rev. D 82, 083517 (2010). arXiv:1006.3418 [astro-ph.CO] ADSCrossRefGoogle Scholar
  25. 25.
    M. Manera, D.F. Mota, Mon. Not. R. Astron. Soc. 371, 1373 (2006). astro-ph/0504519 ADSCrossRefGoogle Scholar
  26. 26.
    S. Basilakos, M. Plionis, J. Sola, Phys. Rev. D 80, 083511 (2009). arXiv:0907.4555 [astro-ph.CO] ADSCrossRefGoogle Scholar
  27. 27.
    J. Grande, J. Sola, S. Basilakos, M. Plionis, J. Cosmol. Astropart. Phys. 1108, 007 (2011). arXiv:1103.4632 [astro-ph.CO] ADSCrossRefGoogle Scholar
  28. 28.
    N.A. Bahcall, X.-h. Fan, Astrophys. J. 504, 1 (1998). arXiv:astro-ph/9803277 ADSCrossRefGoogle Scholar
  29. 29.
    N.A. Bahcall, P. Bode, Astrophys. J. 588, L1 (2003). arXiv:astro-ph/0212363 ADSCrossRefGoogle Scholar
  30. 30.
    M. Chevallier, D. Polarski, Int. J. Mod. Phys. D 10, 213 (2001). arXiv:gr-qc/0009008 ADSCrossRefGoogle Scholar
  31. 31.
    E.V. Linder, Phys. Rev. Lett. 90, 091301 (2003). arXiv:astro-ph/0208512 ADSCrossRefGoogle Scholar
  32. 32.
    L.R. Abramo, R.C. Batista, R. Rosenfeld, J. Cosmol. Astropart. Phys. 0907, 040 (2009). arXiv:0902.3226 [astro-ph.CO] ADSCrossRefGoogle Scholar
  33. 33.
    S. Podariu, T. Souradeep, J.R. Gott, B. Ratra, M.S. Vogeley, Astrophys. J. 559, 9 (2001). arXiv:astro-ph/0102264 ADSCrossRefGoogle Scholar
  34. 34.
    E. Komatsu et al. (WMAP Collaboration), Astrophys. J. Suppl. Ser. 192, 18 (2011). arXiv:1001.4538 [astro-ph.CO] ADSCrossRefGoogle Scholar
  35. 35.
    W.H. Press, P. Schechter, Astrophys. J. 187, 425 (1974) ADSCrossRefGoogle Scholar
  36. 36.
    R.K. Sheth, G. Tormen, Mon. Not. R. Astron. Soc. 308, 119 (1999). arXiv:astro-ph/9901122 ADSCrossRefGoogle Scholar
  37. 37.
    D.J. Eisenstein, W. Hu, Astrophys. J. 496, 605 (1998). arXiv:astro-ph/9709112 ADSCrossRefGoogle Scholar
  38. 38.
    Y. Ikebe, T.H. Reiprich, H. Boehringer, Y. Tanaka, T. Kitayama, Astron. Astrophys. 383, 773 (2002). arXiv:astro-ph/0112315 ADSCrossRefGoogle Scholar
  39. 39.
    J.P. Henry, Astrophys. J. 534, 565 (2000). arXiv:astro-ph/0002365 ADSCrossRefGoogle Scholar
  40. 40.
    M. Schmidt, Astrophys. J. 151, 393 (1968) ADSCrossRefGoogle Scholar
  41. 41.
    Y. Avni, J.N. Bahcall, Astrophys. J. 235, 694 (1980) ADSCrossRefGoogle Scholar
  42. 42.
    M. Donahue, G.M. Voit, I.M. Gioia, G. Luppino, J.P. Hughes, J.T. Stocke, arXiv:astro-ph/9707010
  43. 43.
    J. Hjorth, J. Oukbir, E. van Kampen, New Astron. Rev. 42, 145 (1998) ADSCrossRefGoogle Scholar
  44. 44.
    J. Hjorth, J. Oukbir, E. van Kampen, Mon. Not. R. Astron. Soc. 298, L1 (1998). arXiv:astro-ph/9802293 ADSCrossRefGoogle Scholar
  45. 45.
    P.E.J. Nulsen, S.L. Powell, A. Vikhlinin, Astrophys. J. 722, 55 (2010). arXiv:1008.2393 [astro-ph.CO] ADSCrossRefGoogle Scholar
  46. 46.
    G.L. Fogli, E. Lisi, A. Marrone, D. Montanino, A. Palazzo, Phys. Rev. D 66, 053010 (2002). arXiv:hep-ph/0206162 ADSCrossRefGoogle Scholar
  47. 47.
    E. Gaztañaga, A. Cabré, L. Hui, Mon. Not. R. Astron. Soc. 399, 1663 (2009). arXiv:0807.3551 [astro-ph] ADSCrossRefGoogle Scholar
  48. 48.
    L. Samushia, B. Ratra, Astrophys. J. 701, 1373 (2009). arXiv:0810.2104 [astro-ph] ADSCrossRefGoogle Scholar
  49. 49.
    Y. Wang, Mod. Phys. Lett. A 25, 3093 (2010), and references therein, arXiv:0904.2218 [astro-ph.CO] ADSMATHCrossRefGoogle Scholar
  50. 50.
    W.J. Percival et al. (SDSS Collaboration), Mon. Not. R. Astron. Soc. 401, 2148 (2010). arXiv:0907.1660 [astro-ph.CO] ADSCrossRefGoogle Scholar
  51. 51.
    E.W. Kolb, M.S. Turner, The Early Universe (Addison-Wesley, Redwood City, 1990) Google Scholar
  52. 52.
    P.S. Corasaniti, A. Melchiorri, Phys. Rev. D 77, 103507 (2008). arXiv:0711.4119 [astro-ph] ADSCrossRefGoogle Scholar
  53. 53.
    G. Chen, B. Ratra, Publ. Astron. Soc. Pac. 123, 1127 (2011). arXiv:1105.5206 [astro-ph.CO] ADSCrossRefGoogle Scholar
  54. 54.
    G. Chen, J.R. Gott, B. Ratra, Publ. Astron. Soc. Pac. 115, 1269 (2003). arXiv:astro-ph/0308099 ADSCrossRefGoogle Scholar
  55. 55.
    G.A. Tamman, A. Sandage, B. Reindl, Astron. Astrophys. Rev. 15, 289 (2008). arXiv:0806.3018 [astro-ph] ADSCrossRefGoogle Scholar
  56. 56.
    W.L. Freedman, B.F. Madore, Annu. Rev. Astron. Astrophys. 48, 673 (2010). arXiv:1004.1856 [astro-ph.CO] ADSCrossRefGoogle Scholar
  57. 57.
    R. Jimenez, A. Loeb, Astrophys. J. 573, 37 (2002). arXiv:astro-ph/0106145 ADSCrossRefGoogle Scholar
  58. 58.
    D. Stern, R. Jimenez, L. Verde, M. Kamionkowski, S.A. Stanford, J. Cosmol. Astropart. Phys. 1002, 008 (2010). arXiv:0907.3149 [astro-ph.CO] ADSCrossRefGoogle Scholar
  59. 59.
    E. Gaztañaga, A. Cabré, L. Hui, Mon. Not. R. Astron. Soc. 399, 1663 (2009). arXiv:0807.3551 [astro-ph] ADSCrossRefGoogle Scholar
  60. 60.
    L. Samushia, B. Ratra, Astrophys. J. Lett. 650, L5 (2006). arXiv:astro-ph/0607301 ADSCrossRefGoogle Scholar
  61. 61.
    H. Zhang, Z.-H. Zhu, J. Cosmol. Astropart. Phys. 0803, 007 (2008). arXiv:astro-ph/0703245 ADSCrossRefGoogle Scholar
  62. 62.
    A.A. Sen, R.J. Scherrer, Phys. Lett. B 659, 457 (2008). arXiv:astro-ph/0703416 ADSCrossRefGoogle Scholar
  63. 63.
    L. Samushia, G. Chen, B. Ratra, arXiv:0706.1963 [astro-ph]
  64. 64.
    N. Pan, Y. Gong, Y. Chen, Z.-H. Zhu, Class. Quantum Gravity 27, 155015 (2010). arXiv:1005.4249 [astro-ph.CO] ADSCrossRefMathSciNetGoogle Scholar
  65. 65.
    Y. Chen, B. Ratra, Phys. Lett. B 703, 406 (2011), and references therein. arXiv:1106.4294 [astro-ph.CO] ADSCrossRefGoogle Scholar
  66. 66.
    R. Amanullah et al., Astrophys. J. 716, 712 (2010). arXiv:1004.1711 [astro-ph.CO] ADSCrossRefGoogle Scholar
  67. 67.
    J. Guy et al., Astron. Astrophys. 466, 11 (2007). arXiv:astro-ph/0701828 ADSCrossRefGoogle Scholar
  68. 68.
    A. Lewis, S. Bridle, Phys. Rev. D 66, 103511 (2002). arXiv:astro-ph/0205436 ADSCrossRefGoogle Scholar
  69. 69.
    L. Campanelli, P. Cea, G.L. Fogli, A. Marrone, Phys. Rev. D 83, 103503 (2011). arXiv:1012.5596 [astro-ph.CO] ADSCrossRefGoogle Scholar
  70. 70.
    K.-H. Chae, G. Chen, B. Ratra, D.-W. Lee, Astrophys. J. Lett. 607, L71 (2004). arXiv:astro-ph/0403256 ADSCrossRefGoogle Scholar
  71. 71.
    S. Lee, K.-W. Ng, Phys. Rev. D 76, 043518 (2007). arXiv:0707.1730 [astro-ph] ADSCrossRefGoogle Scholar
  72. 72.
    M. Yashar, B. Bozek, A. Abrahamse, A. Albrecht, M. Barnard, Phys. Rev. D 79, 103004 (2009). arXiv:0811.2253 [astro-ph] ADSCrossRefGoogle Scholar
  73. 73.
    M. Biesiada, A. Piorkowska, B. Malec, Mon. Not. R. Astron. Soc. 406, 1055 (2010), and references therein. arXiv:1105.0946 [astro-ph.CO] ADSGoogle Scholar
  74. 74.
    S. Eidelman et al. (Particle Data Group), Phys. Lett. B 592, 1 (2004) ADSCrossRefGoogle Scholar
  75. 75.
    P. Schuecker, H. Bohringer, C.A. Collins, L. Guzzo, Astron. Astrophys. 398, 867 (2003). arXiv:astro-ph/0208251 ADSCrossRefGoogle Scholar
  76. 76.
    A.G. Riess et al., Astrophys. J. 730, 119 (2011) [Erratum-ibid. 732, 129 (2011)]. arXiv:1103.2976 [astro-ph.CO] ADSCrossRefGoogle Scholar
  77. 77.
    L.I. Gurvits, K.I. Kellermann, S. Frey, Astron. Astrophys. 342, 378 (1999). arXiv:astro-ph/9812018 ADSGoogle Scholar
  78. 78.
    E.J. Guerra, R.A. Daly, L. Wan, Astrophys. J. 544, 659 (2000). arXiv:astro-ph/0006454 ADSCrossRefGoogle Scholar
  79. 79.
    G. Chen, B. Ratra, Astrophys. J. 582, 586 (2003). arXiv:astro-ph/0207051 ADSCrossRefGoogle Scholar
  80. 80.
    M. Bonamente, M.K. Joy, S.J. La Roque, J.E. Carlstrom, E.D. Reese, K.S. Dawson, Astrophys. J. 647, 25 (2006). arXiv:astro-ph/0512349 ADSCrossRefGoogle Scholar
  81. 81.
    Y. Chen, B. Ratra, arXiv:1105.5660 [astro-ph.CO], and references therein
  82. 82.
    S. Capozziello, V.F. Cardone, M. Funaro, S. Andreon, Phys. Rev. D 70, 123501 (2004). arXiv:astro-ph/0410268 ADSCrossRefGoogle Scholar
  83. 83.
    N. Pires, Z.-H. Zhu, J.S. Alcaniz, Phys. Rev. D 73, 123530 (2006). arXiv:astro-ph/0606689 ADSCrossRefGoogle Scholar
  84. 84.
    L. Samushia, A. Dev, D. Jain, B. Ratra, Phys. Lett. B 693, 509 (2010). arXiv:0906.2734 [astro-ph.CO] ADSCrossRefGoogle Scholar
  85. 85.
    M.A. Dantas, J.S. Alcaniz, D. Mania, B. Ratra, Phys. Lett. B 699, 239 (2011), and references therein. arXiv:1010.0995 [astro-ph.CO] ADSCrossRefGoogle Scholar
  86. 86.
    S.W. Allen, D.A. Rapetti, R.W. Schmidt, H. Ebeling, G. Morris, A.C. Fabian, Mon. Not. R. Astron. Soc. 383, 879 (2008). arXiv:0706.0033 [astro-ph] ADSCrossRefGoogle Scholar
  87. 87.
    L. Samushia, B. Ratra, Astrophys. J. Lett. 680, L1 (2008). arXiv:0803.3775 [astro-ph] ADSCrossRefGoogle Scholar
  88. 88.
    S. Ettori et al., Astron. Astrophys. 501, 61 (2009), and references therein. arXiv:0904.2740 [astro-ph.CO] ADSCrossRefGoogle Scholar
  89. 89.
    B.E. Schaefer, Astrophys. J. 660, 16 (2007). arXiv:astro-ph/0612285 ADSCrossRefGoogle Scholar
  90. 90.
    N. Liang, S.N. Zhang, AIP Conf. Proc. 1065, 367 (2008). arXiv:0808.2655 [astro-ph] ADSCrossRefGoogle Scholar
  91. 91.
    Y. Wang, Phys. Rev. D 78, 123532 (2008). arXiv:0809.0657 [astro-ph] ADSCrossRefGoogle Scholar
  92. 92.
    L. Samushia, B. Ratra, Astrophys. J. 714, 1347 (2010), and references therein. arXiv:0905.3836 [astro-ph.CO] ADSCrossRefGoogle Scholar
  93. 93.
    V. Barger, E. Guarnaccia, D. Marfatia, Phys. Lett. B 635, 61 (2006). arXiv:hep-ph/0512320 ADSCrossRefGoogle Scholar
  94. 94.
    R.R. Caldwell, E.V. Linder, Phys. Rev. Lett. 95, 141301 (2005). arXiv:astro-ph/0505494 ADSCrossRefGoogle Scholar
  95. 95.
    G. Gupta, S. Majumdar, A.A. Sen, Mon. Not. R. Astron. Soc. 420, 1309 (2012). arXiv:1109.4112 [astro-ph.CO] ADSCrossRefGoogle Scholar
  96. 96.
    R.J. Scherrer, Phys. Rev. D 73, 043502 (2006). arXiv:astro-ph/0509890 ADSCrossRefMathSciNetGoogle Scholar
  97. 97.
    C. Armendariz-Picon, V.F. Mukhanov, P.J. Steinhardt, Phys. Rev. Lett. 85, 4438 (2000). arXiv:astro-ph/0004134 ADSCrossRefGoogle Scholar
  98. 98.
    T. Chiba, Phys. Rev. D 73, 063501 (2006) [Erratum-ibid. D 80, 129901 (2009)]. arXiv:astro-ph/0510598 ADSCrossRefGoogle Scholar
  99. 99.
    A.Y. Kamenshchik, U. Moschella, V. Pasquier, Phys. Lett. B 511, 265 (2001). arXiv:gr-qc/0103004 ADSMATHCrossRefGoogle Scholar
  100. 100.
    M.C. Bento, O. Bertolami, A.A. Sen, Phys. Rev. D 66, 043507 (2002). arXiv:gr-qc/0202064 ADSCrossRefGoogle Scholar
  101. 101.
    B. Ratra, Phys. Rev. D 43, 3802 (1991) ADSCrossRefGoogle Scholar
  102. 102.
    S. Podariu, B. Ratra, Astrophys. J. 532, 109 (2000). arXiv:astro-ph/9910527 ADSCrossRefGoogle Scholar
  103. 103.
    F. Pace, J.C. Waizmann, M. Bartelmann, arXiv:1005.0233 [astro-ph.CO]
  104. 104.
    D.F. Mota, J. Cosmol. Astropart. Phys. 0809, 006 (2008). arXiv:0812.4493 [astro-ph] ADSCrossRefGoogle Scholar
  105. 105.
    J.F. Navarro, C.S. Frenk, S.D.M. White, Mon. Not. R. Astron. Soc. 275, 720 (1995). arXiv:astro-ph/9408069 ADSGoogle Scholar
  106. 106.
    J.S. Bullock et al., Mon. Not. R. Astron. Soc. 321, 559 (2001). arXiv:astro-ph/9908159 ADSCrossRefGoogle Scholar
  107. 107.
    P. Wang, Astrophys. J. 640, 18 (2006). arXiv:astro-ph/0507195 ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2012

Authors and Affiliations

  • L. Campanelli
    • 1
  • G. L. Fogli
    • 1
    • 2
  • T. Kahniashvili
    • 3
    • 4
    • 5
  • A. Marrone
    • 1
    • 2
  • Bharat Ratra
    • 6
  1. 1.Dipartimento di FisicaUniversità di BariBariItaly
  2. 2.INFN-Sezione di BariBariItaly
  3. 3.McWilliams Center for Cosmology and Department of PhysicsCarnegie Mellon UniversityPittsburghUSA
  4. 4.Department of PhysicsLaurentian UniversitySudburyCanada
  5. 5.Abastumani Astrophysical ObservatoryIlia State UniversityTbilisiGeorgia
  6. 6.Department of PhysicsKansas State UniversityManhattanUSA

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