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Chinese Physics C> 2015, Vol. 39> Issue(5) : 055101 DOI: 10.1088/1674-1137/39/5/055101

Quadrupole-octopole alignment of CMB related to the primordial power spectrum with dipolar modulation in anisotropic spacetime

  • The WMAP and Planck observations show that the quadrupole and octopole orientations of the CMB might align with each other. We reveal that the quadrupole-octopole alignment is a natural implication of the primordial power spectrum in an anisotropic spacetime. The primordial power spectrum is presented with a dipolar modulation. We obtain the privileged plane by employing the “power tensor” technique. At this plane, there is maximum correlation between quadrupole and octopole. The probability for the alignment is much larger than that in the isotropic universe. We find that this model would lead to deviations from the statistical isotropy only for low-l multipoles.

  • References

    [1] WMAP collaboration. arXiv:1212.5225[2] Planck collaboration. arXiv:1303.5083[3] WMAP collaboration. Astrophys. J. Suppl., 2003, 148: 1[4] Tegmark M, de Oliveira-Costa A, Hamilton A. Phys. Rev. D, 2003, 68: 123523[5] Schwarz D J, Starkman G D, Huterer D et al. Phys. Rev. Lett., 2004, 93: 221301[6] Copi C J, Huterer D, Starkman G D. Phys. Rev. D, 2004 70: 043515[7] Copi C J, Huterer D, Schwarz D J et al. MNRAS, 2006, 367: 79[8] Eriksen H K, Hansen F K, Banday A J et al. Astrophys. J., 2004, 605: 14[9] Hansen F K, Banday A J, Gorski K M. MNRAS, 2004, 354: 641[10] Park C G. MNRAS, 2004, 349: 313[11] Land K, Magueijo J. Phys. Rev. D, 2005, 72: 101302[12] Kim J, Naselsky P. Astrophys. J., 2010, 714: L265[13] Naselsky P, Zhao W, Kim J et al. Astrophys. J., 2012, 749: 31[14] Kim J, Naselsky P. Phys. Rev. D, 2010, 82: 063002[15] Gruppuso A et al. MNRAS, 2011, 411: 1445[16] Longo M J. Phys. Lett. B, 2011, 699: 224[17] Shamir L. Phys. Lett. B, 2012, 715: 25[18] Aluri P K, Jain P. MNRAS, 2012, 419: 3378[19] Gurzadyan V, Starobinsky A, Kashin A et al. Mod. Phys. Lett. A, 2007, 22: 2955[20] Ben-David A, Kovetz E D, Itzhaki N. Astrophys. J., 2012, 748: 39[21] Finelli F, Gruppuso A, Paci F et al. JCAP, 2012, 07: 049[22] ZHAO W. arXiv:1306.0955[23] Gordon C, HU W, Huterer D et al. Phys. Rev. D, 2005, 72: 103002[24] Eriksen H K, Banday A J, Gorski K M et al. Astrophys. J., 2007, 660: L81[25] Hoftuft J et al. Astrophys. J., 2009, 699: 985[26] Hanson D, Lewis A. Phys. Rev. D, 2009, 80: 063004[27] Ralston J P, Jain P. Int. J. Mod. Phys. D, 2004, 13: 1857[28] Samal P K, Saha R, Jain P et al. MNRAS, 2008, 385: 1718[29] Rath P K, Mudholkar T, Jain P et al. JCAP, 2013, 04: 007[30] CHANG Z, WANG S. Eur. Phys. J. C, 2013, 73: 2516[31] Randers G. Phys. Rev., 1941, 59: 195[32] Cohen A G, Glashow S L. Phys. Rev. Lett., 2006, 97: 021601[33] LI X, CHANG Z. Differ. Geom. Appl., 2012, 30: 737[34] ZHANG L, XUE X. arXiv:1205.1134[35] Finsler P. ber Kurven and Flchen in allgemeinen Rumen (Ph.D. Thesis). Gttingan, 1918. Basel: Birkhuser Verlag, 1951[36] BAO D, Chern S S, SHEN Z. An Introduction to Riemann-Finsler Geometry. New York: Springer, 2000[37] WANG H C. J. London Math. Soc., 1947, s1-22 (1): 5[38] Rutz S F. Contemp. Math., 1996, 196: 289[39] Erickcek A L, Kamionkowski M, Carroll S M. Phys. Rev. D, 2008, 78: 123520[40] Lyth D H. arXiv:1304.1270[41] WANG L, Mazumdar A. Phys. Rev. D, 2013, 88: 023512[42] Mazumdar A, WANG L. arXiv:1306.5736[43] Baghram S, Namjoo M H, Firouzjahi H. arXiv:1303.4368[44] Namjoo M H, Baghram S, Firouzjahi H. arXiv:1305.0813[45] Abolhasani A A, Baghram S, Firouzjahi H et al. arXiv:1306.6932[46] Ohashi J, Soda J, Tsujikawa S. Phys. Rev. D, 2013, 87: 083520[47] CAI Y F, ZHAO W, ZHANG Y. arXiv:1307.4090[48] Rund H. The Differential Geometry of Finsler Spaces. Berlin: Springer, 1959[49] Asanov G S. Finsler Geometry, Relativity and Gauge Theories. Dordrecht: Reidel, 1995[50] Stavrinos P C, Kouretsis A P, Stathakopoulos M. Gen. Relativ. Gravit., 2008, 40: 1403[51] Starobinsky A A. Phys. Lett. B, 1980, 91: 99[52] Guth A H. Phys. Rev. D, 1981, 23: 347[53] Linde A D. Phys. Lett. B, 1982, 108: 389[54] Albrecht A, Steinhardt P J. Phys. Rev. Lett., 1982, 48: 1220[55] Linde A D. Phys. Lett. B, 1983, 129: 177[56] Watanabe M, Kanno S, Soda J. MNRAS, 2011, 412: L83[57] Mukhanov V F, Chibisov G. JETP Lett., 1981, 33: 532[58] Mukhanov V F, Chibisov G. Sov. Phys. JETP, 1982, 56: 258[59] Hawking S. Phys. Lett. B, 1982, 115: 295[60] Guth A H, Pi S. Phys. Rev. Lett., 1982, 49: 1110[61] Starobinsky A A. Phys. Lett. B, 1982, 117: 175[62] Bardeen J M, Steinhardt P J, Turner M S. Phys. Rev. D, 1983, 28: 679[63] Mukhanov V F. JETP Lett., 1985, 41: 493[64] Mazumdar A, Rocher J. Phys. Rept., 2011, 497: 85[65] WANG L, Pukartas E, Mazumdar A. JCAP, 2013, 07: 019[66] Gumrukcuoglu A E, Contaldi C R, Peloso M. JCAP, 2007, 11: 005

  • References

    [1] WMAP collaboration. arXiv:1212.5225[2] Planck collaboration. arXiv:1303.5083[3] WMAP collaboration. Astrophys. J. Suppl., 2003, 148: 1[4] Tegmark M, de Oliveira-Costa A, Hamilton A. Phys. Rev. D, 2003, 68: 123523[5] Schwarz D J, Starkman G D, Huterer D et al. Phys. Rev. Lett., 2004, 93: 221301[6] Copi C J, Huterer D, Starkman G D. Phys. Rev. D, 2004 70: 043515[7] Copi C J, Huterer D, Schwarz D J et al. MNRAS, 2006, 367: 79[8] Eriksen H K, Hansen F K, Banday A J et al. Astrophys. J., 2004, 605: 14[9] Hansen F K, Banday A J, Gorski K M. MNRAS, 2004, 354: 641[10] Park C G. MNRAS, 2004, 349: 313[11] Land K, Magueijo J. Phys. Rev. D, 2005, 72: 101302[12] Kim J, Naselsky P. Astrophys. J., 2010, 714: L265[13] Naselsky P, Zhao W, Kim J et al. Astrophys. J., 2012, 749: 31[14] Kim J, Naselsky P. Phys. Rev. D, 2010, 82: 063002[15] Gruppuso A et al. MNRAS, 2011, 411: 1445[16] Longo M J. Phys. Lett. B, 2011, 699: 224[17] Shamir L. Phys. Lett. B, 2012, 715: 25[18] Aluri P K, Jain P. MNRAS, 2012, 419: 3378[19] Gurzadyan V, Starobinsky A, Kashin A et al. Mod. Phys. Lett. A, 2007, 22: 2955[20] Ben-David A, Kovetz E D, Itzhaki N. Astrophys. J., 2012, 748: 39[21] Finelli F, Gruppuso A, Paci F et al. JCAP, 2012, 07: 049[22] ZHAO W. arXiv:1306.0955[23] Gordon C, HU W, Huterer D et al. Phys. Rev. D, 2005, 72: 103002[24] Eriksen H K, Banday A J, Gorski K M et al. Astrophys. J., 2007, 660: L81[25] Hoftuft J et al. Astrophys. J., 2009, 699: 985[26] Hanson D, Lewis A. Phys. Rev. D, 2009, 80: 063004[27] Ralston J P, Jain P. Int. J. Mod. Phys. D, 2004, 13: 1857[28] Samal P K, Saha R, Jain P et al. MNRAS, 2008, 385: 1718[29] Rath P K, Mudholkar T, Jain P et al. JCAP, 2013, 04: 007[30] CHANG Z, WANG S. Eur. Phys. J. C, 2013, 73: 2516[31] Randers G. Phys. Rev., 1941, 59: 195[32] Cohen A G, Glashow S L. Phys. Rev. Lett., 2006, 97: 021601[33] LI X, CHANG Z. Differ. Geom. Appl., 2012, 30: 737[34] ZHANG L, XUE X. arXiv:1205.1134[35] Finsler P. ber Kurven and Flchen in allgemeinen Rumen (Ph.D. Thesis). Gttingan, 1918. Basel: Birkhuser Verlag, 1951[36] BAO D, Chern S S, SHEN Z. An Introduction to Riemann-Finsler Geometry. New York: Springer, 2000[37] WANG H C. J. London Math. Soc., 1947, s1-22 (1): 5[38] Rutz S F. Contemp. Math., 1996, 196: 289[39] Erickcek A L, Kamionkowski M, Carroll S M. Phys. Rev. D, 2008, 78: 123520[40] Lyth D H. arXiv:1304.1270[41] WANG L, Mazumdar A. Phys. Rev. D, 2013, 88: 023512[42] Mazumdar A, WANG L. arXiv:1306.5736[43] Baghram S, Namjoo M H, Firouzjahi H. arXiv:1303.4368[44] Namjoo M H, Baghram S, Firouzjahi H. arXiv:1305.0813[45] Abolhasani A A, Baghram S, Firouzjahi H et al. arXiv:1306.6932[46] Ohashi J, Soda J, Tsujikawa S. Phys. Rev. D, 2013, 87: 083520[47] CAI Y F, ZHAO W, ZHANG Y. arXiv:1307.4090[48] Rund H. The Differential Geometry of Finsler Spaces. Berlin: Springer, 1959[49] Asanov G S. Finsler Geometry, Relativity and Gauge Theories. Dordrecht: Reidel, 1995[50] Stavrinos P C, Kouretsis A P, Stathakopoulos M. Gen. Relativ. Gravit., 2008, 40: 1403[51] Starobinsky A A. Phys. Lett. B, 1980, 91: 99[52] Guth A H. Phys. Rev. D, 1981, 23: 347[53] Linde A D. Phys. Lett. B, 1982, 108: 389[54] Albrecht A, Steinhardt P J. Phys. Rev. Lett., 1982, 48: 1220[55] Linde A D. Phys. Lett. B, 1983, 129: 177[56] Watanabe M, Kanno S, Soda J. MNRAS, 2011, 412: L83[57] Mukhanov V F, Chibisov G. JETP Lett., 1981, 33: 532[58] Mukhanov V F, Chibisov G. Sov. Phys. JETP, 1982, 56: 258[59] Hawking S. Phys. Lett. B, 1982, 115: 295[60] Guth A H, Pi S. Phys. Rev. Lett., 1982, 49: 1110[61] Starobinsky A A. Phys. Lett. B, 1982, 117: 175[62] Bardeen J M, Steinhardt P J, Turner M S. Phys. Rev. D, 1983, 28: 679[63] Mukhanov V F. JETP Lett., 1985, 41: 493[64] Mazumdar A, Rocher J. Phys. Rept., 2011, 497: 85[65] WANG L, Pukartas E, Mazumdar A. JCAP, 2013, 07: 019[66] Gumrukcuoglu A E, Contaldi C R, Peloso M. JCAP, 2007, 11: 005

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Get Citation
CHANG Zhe, LI Xin and WANG Sai. Quadrupole-octopole alignment of CMB related to the primordial power spectrum with dipolar modulation in anisotropic spacetime[J]. Chinese Physics C, 2015, 39(5): 055101. doi: 10.1088/1674-1137/39/5/055101
CHANG Zhe, LI Xin and WANG Sai. Quadrupole-octopole alignment of CMB related to the primordial power spectrum with dipolar modulation in anisotropic spacetime[J]. Chinese Physics C, 2015, 39(5): 055101.  doi: 10.1088/1674-1137/39/5/055101 shu
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Received: 2014-05-20
Revised: 2014-11-06
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Quadrupole-octopole alignment of CMB related to the primordial power spectrum with dipolar modulation in anisotropic spacetime

    Corresponding author: CHANG Zhe,
    Corresponding author: LI Xin,
    Corresponding author: WANG Sai,
  • Received Date: 2014-05-20
  • Accepted Date: 2014-11-06
  • Available Online: 2015-05-05

Abstract: The WMAP and Planck observations show that the quadrupole and octopole orientations of the CMB might align with each other. We reveal that the quadrupole-octopole alignment is a natural implication of the primordial power spectrum in an anisotropic spacetime. The primordial power spectrum is presented with a dipolar modulation. We obtain the privileged plane by employing the “power tensor” technique. At this plane, there is maximum correlation between quadrupole and octopole. The probability for the alignment is much larger than that in the isotropic universe. We find that this model would lead to deviations from the statistical isotropy only for low-l multipoles.

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