Abstract
This article describes the 1+3 covariant approach to the study of CMB anisotropies using relativistic kinetic theory. We derive a complete set of frame - independent nonlinear equations for the Boltzmann radiation multipole hierarchy and linearise them about a Friedmann-Robertson-Walker model. Particular emphasis is given to the line of sight or null integration of the Boltzmann equation and how it compares to the usual time-like integrations presented in much of the CMB literature. We also discuss the calculation of CMB anisotropies in Bianchi models and how these studies affect the almost - Ehlers-Geren-Sachs result, crucial to foundations to modern CMB calculations.
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References
R K Sachs and A M Wolfe, Astrophys. J. 147, 73 (1967).
C J Hogan, N Kaiser and M J Rees, Philos. Trans. R. Soc. London A307, 97 (1982).
M Panek, Phys. Rev. D 34, 416 (1986).
W R Stoeger, C-M Xu, G F R Ellis, and M Katz, Astrophys. J. 445, 17 (1995).
W R Stoeger, G F R Ellis, and B G Schmidt, Gen. Relativ. Gravit. 23, 1169 (1991).
S W Hawking, Ap. J. 145, 544 (1966).
G F R Ellis, in General Relativity and Cosmology, Proceedings of the XLVII Enrico Fermi Summer School, Ed. R K Sachs (Academic Press, New York, 1971).
J Ehlers, in General Relativity and Cosmology, Proceedings of the XLVII Enrico Fermi Summer School, Ed. R K Sachs (Academic Press, New York, 1971).
A Challinor, PhD Thesis (Cambridge University, 1997).
P K S Dunsby, M Bruni and G F R Ellis, Ap. J., 395, 54 (1992).
R Maartens, T Gebbie and G F R Ellis, Cosmic microwave background anisotropies: nonlinear dynamics. Preprint astro-ph/9808163, (1998).
R W Lindquist, Ann. Phys. 37, 487 (1966).
J M Stewart, Non Equilibrium Relativistic Kinetic Theory, Springer Lecture Notes in Physics 10 (Springer, Berlin, 1971).
G F R Ellis, D R Matravers and R Treciokas, Ann. Phys. 150, 455 (1983).
G F R Ellis, R Treciokas and D R Matravers, Ann. Phys. 150, 487 (1983).
F A E Pirani, in Lectures in General Relativity, Eds. S Deser and K Ford (Prentice-Hall, Englewood Cliffs, 1964).
K S Thorne, Rev. Mod. Phys. 52, 299 (1980).
J Ehlers, P Geren and R K Sachs, J. Math. Phys. 9, 1344 (1968).
R Treciokas and G F R Ellis, Commun. Math. Phys. 23, 1 (1971).
M L Wilson, Astrophys. J. 273, 2 (1983).
T Gebbie and G F R Ellis, Covariant cosmic microwave background anisotropies. I: Algebraic relations for mode and multipole representations. astro-ph/9804916. To appear in Ann. Phys. (2000).
A D Challinor and A N Lasenby, Cosmic microwave background anisotropies in the CDM model: A covariant and gauge-invariant approach. Preprint astrro-ph/9804301, (1998).
R Maartens, G F R Ellis and W J Stoeger, Phys. Rev. D 51, 1525 (1995); Phys. Rev. D 51, 5942 (1995).
W Hu and N Sugiyama, Phys. Rev. D 51, 2599 (1995).
M Bruni, P K S Dunsby and G F R Ellis, Astrophys. J. 395, 34 (1992).
T Gebbie, P K S Dunsby and G F R Ellis: Covariant cosmic microwave background anisotropies II: the almost-Friedmaan-Lemâtre model, To appear in Ann. Phys (2000).
A Challinor: Improved treatment of microwave background polarization in cosmological models, astro-ph/9911481 (1999).
A Lewis, A Challinor and A Lasenby: Efficient computation of CMB anisotropies in closed FRW models, astro-ph/9911177 (1999).
W Hu and M White, Astrophys. J. 471, 30 (1996).
A Challinor and A Lasenby, Phys. Rev. D 58 023001 (1998).
P K S Dunsby, Class. Quantum. Grav. 14, 3391 (1997).
[32] E. R. Harrison, Vistas in Astronomy 2, 241 (1977).
P K S Dunsby, T Gebbie and G F R Ellis, Null and time-like analysis of cosmic background radiation anisotropies. In preparation (2000).
U S Nilsson, C Uggla, and J Wainwright: A dynamical systems approach to geodesics in Bianchi cosmologies, gr-qc/9908062 (1999).
U S Nilsson, W C Lim, C Uggla, and J Wainwright: An almost isotropic cosmic microwave background temperature does not imply an almost isotropic universe. Ap J Lett 522, L1 (1999), astro-ph/9904252.
W C Lim, U S Nilsson and J Wainwright: Anisotropic Universes with isotropic cosmic microwave background radiation, gr-qc/9912001 (1999).
W Stoeger, R Maartens and G F R Ellis: Proving almost-homogeneity of the universe: an almost-Ehlers, Geren and Sachs theorem. Ap J 443, 1 (1995).
G F R Ellis, R Maartens, and S D Nel: “The expansion of the universe”. Man Not Roy Ast Soc 184, 439 (1978).
C Clarkson and R Barrett, gr-qc/9906097 (1999).
R Barrett and C Clarkson, gr-qc/9911235 (1999).
M Goliath and G F R Ellis, Phys Rev D 60, 023502 (1999),gr-qc/9811068.
H van Elst and G F R Ellis. Quasi-Newtonian Dust Cosmologies. CQG 15: 3545 (1998).
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Ellis, G.F.R., Dunsby, P.K.S. (2001). The 1+3 Covariant Approach to CMB Anisotropies. In: Sánchez, N.G. (eds) Current Topics in Astrofundamental Physics: The Cosmic Microwave Background. NATO Science Series, vol 562. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0748-1_9
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DOI: https://doi.org/10.1007/978-94-010-0748-1_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6856-4
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