CMB anisotropies: Total angular momentum method

Wayne Hu; Martin White

doi:10.1103/PhysRevD.56.596

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CMB anisotropies: Total angular momentum method

Wayne Hu

Martin White

Institute for Advanced Study, School of Natural Sciences, Princeton, New Jersey 08540

Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637

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Phys. Rev. D 56, 596 – Published 15 July, 1997

DOI: https://doi.org/10.1103/PhysRevD.56.596

Abstract

A total angular momentum representation simplifies the radiation transport problem for temperature and polarization anisotropy in the cosmic microwave background (CMB). Scattering terms couple only the quadrupole moments of the distributions and each moment corresponds directly to the observable angular pattern on the sky. We develop and employ these techniques to study the general properties of anisotropy generation from scalar, vector, and tensor perturbations to the metric and the matter, both in the cosmological fluids and from any seed perturbations (e.g., defects) that may be present. The simpler, more transparent form and derivation of the Boltzmann equations brings out the geometric and model-independent aspects of temperature and polarization anisotropy formation. Large angle scalar polarization provides a robust means to distinguish between isocurvature and adiabatic models for structure formation in principle. Vector modes have the unique property that the CMB polarization is dominated by magnetic-type parity at small angles (a factor of $6$ in power compared with $0$ for the scalars and $8 / 13$ for the tensors) and hence potentially distinguishable independent of the model for the seed. The tensor modes produce a different sign from the scalars and vectors for the temperature-polarization correlations at large angles. We explore conditions under which one perturbation type may dominate over the others including a detailed treatment of the photon-baryon fluid before recombination.

References (33)

See the MAP site at URL http://map.gsfc.nasa.gov
See the Planck Surveyor site at URL http://astro.estec.esa.nl/SA-general/Projects/Cobras/cobras.html
U. Seljak and M. Zaldarriaga, Phys. Rev. Lett. 78, 2054 (1997); M. Zaldarriaga and U. Seljak, Phys. Rev. D 55, 1830 (1997)
M. Kamionkowski, A. Kosowsky, and A. Stebbins, Phys. Rev. Lett. 78, 2058 (1997); Phys. Rev. D 55, 7368 (1997).
W. Hu and M. White, Report No. (unpublished).
K. Tomita, Prog. Theor. Phys. 68, 310 (1982).
L. F. Abbott and R. K. Schaeffer, Astrophys. J. 308, 546 (1986).
W. Hu, U. Seljak, M. White, and M. Zaldarriaga (in preparation).
R. G. Crittenden, D. Coulson, and N. G. Turok, Phys. Rev. D 52, 5402 (1995); R. G. Crittenden, R. L. Davis, and P. J. Steinhardt, Astrophys. J. Lett. 417, L13 (1993).
A. G. Polnarev, Sov. Astron. 29, 607 (1985).
J. R. Bond and G. Efstathiou, Astrophys. J., Lett. Ed. 285, L45 (1984); Mon. Not. R. Astron. Soc. 226, 655 (1987).
E. Newman and R. Penrose, J. Math. Phys. (N.Y.) 7, 863 (1966); J. N. Goldberg et al., 8, 2155 (1967); K. S. Thorne, Rev. Mod. Phys. 52, 299 (1980).
J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, New York, 1985) p. 215.
J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1972).
H. Kodama and M. Sasaki, Prog. Theor. Phys. 78, 1 (1984).
S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).
J. M. Bardeen, Phys. Rev. D 22, 1882 (1980).
R. Durrer, Phys. Rev. D 42, 2533 (1990).
A. Kosowsky, Ann. Phys. (N.Y.) 246, 49 (1996); A. Melchiorri and N. Vittorio, Report No. (unpublished).
R. K. Sachs and A. M. Wolfe, Astrophys. J. 147, 73 (1967).
There can be a small contribution from unequal time correlations at the very lowest $l$ if the main signal from the last scattering surface is falling sufficiently rapidly.
W. Hu and N. Sugiyama, Astrophys. J. 444, 489 (1995); Phys. Rev. D 51, 2599 (1995).
M. Zaldarriaga and D. Harari, Phys. Rev. D 55, 3276 (1997).
U. Seljak and M. Zaldarriaga, Astrophys. J. 469, 437 (1996).
P. J. E. Peebles and J. T. Yu, Astrophys. J. 162, 815 (1970).
N. Kaiser, Mon. Not. R. Astron. Soc. 202, 1169 (1983).
W. Hu, D. N. Spergel, and M. White, Phys. Rev. D 55, 3288 (1997).
D.N. Spergel and M. Zaldarriaga (in preparation); R. Battye and D. Harrari (in preparation).
W. Hu and M. White, Astrophys. J. 479, 568 (1997); R. Battye, Phys. Rev. D 55, 7361 (1997).
S. Veeraraghavan and A. Stebbins, Astrophys. J. 365, 37 (1990).
N. Turok, Phys. Rev. D 54, 3686 (1996); Phys. Rev. Lett. 77, 4138 (1996).
J. Negroponte and J. Silk, Phys. Rev. Lett. 44, 1433 (1980); M. M. Basko and A. G. Polnarev, Mon. Not. R. Astron. Soc. 191, 207 (1980); C. J. Hogan, N. Kaiser, and M. Rees, Philos. Trans. R. Soc. London, Ser. A 307, 97 (1982).
M. Zaldarriaga, D. N. Spergel, and U. Seljak, Report No. (unpublished).

[c1] See the MAP site at URL http://map.gsfc.nasa.gov

[c2] See the Planck Surveyor site at URL http://astro.estec.esa.nl/SA-general/Projects/Cobras/cobras.html

[c3] U. Seljak and M. Zaldarriaga, Phys. Rev. Lett. 78, 2054 (1997); M. Zaldarriaga and U. Seljak, Phys. Rev. D 55, 1830 (1997)

[c4] M. Kamionkowski, A. Kosowsky, and A. Stebbins, Phys. Rev. Lett. 78, 2058 (1997); Phys. Rev. D 55, 7368 (1997).

[c5] W. Hu and M. White, Report No. (unpublished).

[c6] K. Tomita, Prog. Theor. Phys. 68, 310 (1982).

[c7] L. F. Abbott and R. K. Schaeffer, Astrophys. J. 308, 546 (1986).

[c8] W. Hu, U. Seljak, M. White, and M. Zaldarriaga (in preparation).

[c9] R. G. Crittenden, D. Coulson, and N. G. Turok, Phys. Rev. D 52, 5402 (1995); R. G. Crittenden, R. L. Davis, and P. J. Steinhardt, Astrophys. J. Lett. 417, L13 (1993).

[c10] A. G. Polnarev, Sov. Astron. 29, 607 (1985).

[c11] J. R. Bond and G. Efstathiou, Astrophys. J., Lett. Ed. 285, L45 (1984); Mon. Not. R. Astron. Soc. 226, 655 (1987).

[c12] E. Newman and R. Penrose, J. Math. Phys. (N.Y.) 7, 863 (1966); J. N. Goldberg et al., 8, 2155 (1967); K. S. Thorne, Rev. Mod. Phys. 52, 299 (1980).

[c13] J. J. Sakurai, Modern Quantum Mechanics (Addison-Wesley, New York, 1985) p. 215.

[c14] J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1972).

[c15] H. Kodama and M. Sasaki, Prog. Theor. Phys. 78, 1 (1984).

[c16] S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960).

[c17] J. M. Bardeen, Phys. Rev. D 22, 1882 (1980).

[c18] R. Durrer, Phys. Rev. D 42, 2533 (1990).

[c19] A. Kosowsky, Ann. Phys. (N.Y.) 246, 49 (1996); A. Melchiorri and N. Vittorio, Report No. (unpublished).

[c20] R. K. Sachs and A. M. Wolfe, Astrophys. J. 147, 73 (1967).

[c21] There can be a small contribution from unequal time correlations at the very lowest $l$ if the main signal from the last scattering surface is falling sufficiently rapidly.

[c22] W. Hu and N. Sugiyama, Astrophys. J. 444, 489 (1995); Phys. Rev. D 51, 2599 (1995).

[c23] M. Zaldarriaga and D. Harari, Phys. Rev. D 55, 3276 (1997).

[c24] U. Seljak and M. Zaldarriaga, Astrophys. J. 469, 437 (1996).

[c25] P. J. E. Peebles and J. T. Yu, Astrophys. J. 162, 815 (1970).

[c26] N. Kaiser, Mon. Not. R. Astron. Soc. 202, 1169 (1983).

[c27] W. Hu, D. N. Spergel, and M. White, Phys. Rev. D 55, 3288 (1997).

[c28] D.N. Spergel and M. Zaldarriaga (in preparation); R. Battye and D. Harrari (in preparation).

[c29] W. Hu and M. White, Astrophys. J. 479, 568 (1997); R. Battye, Phys. Rev. D 55, 7361 (1997).

[c30] S. Veeraraghavan and A. Stebbins, Astrophys. J. 365, 37 (1990).

[c31] N. Turok, Phys. Rev. D 54, 3686 (1996); Phys. Rev. Lett. 77, 4138 (1996).

[c32] J. Negroponte and J. Silk, Phys. Rev. Lett. 44, 1433 (1980); M. M. Basko and A. G. Polnarev, Mon. Not. R. Astron. Soc. 191, 207 (1980); C. J. Hogan, N. Kaiser, and M. Rees, Philos. Trans. R. Soc. London, Ser. A 307, 97 (1982).

[c33] M. Zaldarriaga, D. N. Spergel, and U. Seljak, Report No. (unpublished).

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CMB anisotropies: Total angular momentum method

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