Physics of the Cosmic Microwave Background Radiation

  • David Wands
  • Oliver F. Piattella
  • Luciano Casarini
Conference paper
Part of the Astrophysics and Space Science Proceedings book series (ASSSP, volume 45)


The cosmic microwave background (CMB) radiation provides a remarkable window onto the early universe, revealing its composition and structure. In these lectures we review and discuss the physics underlying the main features of the CMB.


Cosmic Microwave Background Cosmic Microwave Background Anisotropy Angular Power Spectrum Cosmic Microwave Background Temperature Cosmic Microwave Background Photon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



DW is grateful to the organisers of the second José Plínio Baptista school for their warm hospitality. The authors are grateful to Rob Crittenden for helpful comments. This work is supported by STFC grants ST/K00090/1 and ST/L005573/1.


  1. Adam, R., et al.: Planck 2015 results. I. Overview of products and scientific results (2015). arXiv:1502.01582
  2. Ade, P.A.R., et al.: Planck 2013 results. I. Overview of products and scientific results. Astron. Astrophys. 571, A1 (2014a). arXiv:1303.5062. doi:10.1051/0004-6361/201321529.
  3. Ade, P.A.R., et al.: Planck 2013 results. XVI. Cosmological parameters. Astron. Astrophys. 571, A16 (2014b). arXiv:1303.5076. doi:10.1051/0004-6361/201321591
  4. Ade, P.A.R., et al.: Planck 2013 results. XVII. Gravitational lensing by large-scale structure. Astron. Astrophys. 571, A17 (2014c). arXiv:1303.5077. doi:10.1051/0004-6361/201321543
  5. Ade, P.A.R., et al.: Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity. Astron. Astrophys. 571, A24 (2014d). arXiv:1303.5084. doi:10.1051/0004-6361/201321554
  6. Ade, P.A.R., et al.: Planck 2015 results. XXIV. Cosmology from Sunyaev-Zeldovich cluster counts (2015). arXiv:1502.01597
  7. Alpher, V.S.: Ralph A. Alpher, George Antonovich Gamow, and the prediction of the cosmic microwave background radiation. Asian J. Phys. 2, 17–26 (2014). arXiv:1411.0172
  8. Alpher, R.A., Bethe, H., Gamow, G.: The origin of chemical elements. Phys. Rev. 73, 803–804 (1948). doi:10.1103/PhysRev.73.803 ADSCrossRefGoogle Scholar
  9. Bardeen, J.M.: Gauge invariant cosmological perturbations. Phys. Rev. D22, 1882–1905 (1980). doi:10.1103/PhysRevD.22.1882 ADSMathSciNetGoogle Scholar
  10. Bartolo, N., Komatsu, E., Matarrese, S., Riotto, A.: Non-Gaussianity from inflation: theory and observations. Phys. Rep. 402, 103–266 (2004). arXiv:astro-ph/0406398. doi:10.1016/j.physrep.2004.08.022
  11. Bleem, L.E., et al.: Galaxy clusters discovered via the Sunyaev-Zel’dovich effect in the 2500-square-degree SPT-SZ survey. Astrophys. J. Suppl. 216 (2), 27 (2015). arXiv:1409.0850. doi:10.1088/0067-0049/216/2/27
  12. Bucher, M., Moodley, K., Turok, N.: The general primordial cosmic perturbation. Phys. Rev. D62, 083508 (2000). arXiv:astro-ph/9904231. doi:10.1103/PhysRevD.62.083508
  13. Chluba, J., Sunyaev, R.A.: The evolution of CMB spectral distortions in the early Universe. Mon. Not. R. Astron. Soc. 419, 1294–1314 (2012). arXiv:1109.6552. doi:10.1111/j.1365-2966.2011.19786.x
  14. Crittenden, R.: (2016). Online. Accessed 7 July 2016
  15. Dodelson, S.: Modern cosmology. Academic (2003)Google Scholar
  16. Fidler, C., Pettinari, G.W., Beneke, M., Crittenden, R., Koyama, K., et al.: The intrinsic B-mode polarisation of the cosmic microwave background. JCAP 1407, 011 (2014). arXiv:1401.3296. doi:10.1088/1475-7516/2014/07/011
  17. Fixsen, D.J., Cheng, E.S., Gales, J.M., Mather, J.C., Shafer, R.A., et al.: The cosmic microwave background spectrum from the full COBE FIRAS data set. Astrophys. J. 473, 576 (1996). arXiv:astro-ph/9605054. doi:10.1086/178173.
  18. Friedmann, A.: On the possibility of a world with constant negative curvature of space. Z. Phys. 21, 326–332 (1924). doi:10.1007/BF01328280 ADSMathSciNetCrossRefGoogle Scholar
  19. Goldberg, D.M., Spergel, D.N.: Microwave background bispectrum. 2. A probe of the low redshift universe. Phys. Rev. D59, 103002 (1999). arXiv:astro-ph/9811251. doi:10.1103/PhysRevD.59.103002
  20. Hasselfield, M., Hilton, M., Marriage, T.A., Addison, G.E., Barrientos, L.F., et al.: The Atacama Cosmology Telescope: Sunyaev-Zel’dovich selected galaxy clusters at 148 GHz from three seasons of data. JCAP 1307, 008 (2013). arXiv:1301.0816. doi:10.1088/1475-7516/2013/07/008
  21. Hu, W.: Lecture Notes on CMB Theory: From Nucleosynthesis to Recombination (2008). arXiv:0802.3688
  22. Hu, W.: (2016). Online. Accessed 29 August 2016
  23. Hu, W., Dodelson, S.: Cosmic microwave background anisotropies. Ann. Rev. Astron. Astrophys. 40, 171–216 (2002). arXiv:astro-ph/0110414. doi:10.1146/annurev.astro.40.060401.093926
  24. Huang, Z., Vernizzi, F.: Cosmic microwave background bispectrum from recombination. Phys. Rev. Lett. 110 (10), 101303 (2013). arXiv:1212.3573. doi:10.1103/PhysRevLett.110.101303
  25. Hubble, E.: A relation between distance and radial velocity among extra-galactic nebulae. Proc. Natl. Acad. Sci. 15, 168–173 (1929). doi:10.1073/pnas.15.3.168 ADSCrossRefzbMATHGoogle Scholar
  26. Klein, O., Nishina, T.: Über die Streuung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac. Zeitschrift fur Physik 52, 853–868 (1929). doi:10.1007/BF01366453 ADSCrossRefzbMATHGoogle Scholar
  27. Komatsu, E.: (2016). Online. Accessed 7 July 2016
  28. Lemaitre, G.: A homogeneous Universe of constant mass and growing radius accounting for the radial velocity of extragalactic nebulae. Ann. Soc. Sci. Brux. Ser. I Sci. Math. Astron. Phys. A47, 49–59 (1927). doi:10.1007/s10714-013-1548-3 Google Scholar
  29. Lesgourgues, J.: The Cosmic Linear Anisotropy Solving System (CLASS) I: Overview (2011). arXiv:1104.2932
  30. Lewis, A., Challinor, A., Lasenby, A.: Efficient computation of CMB anisotropies in closed FRW models. Astrophys. J. 538, 473–476 (2000). arXiv:astro-ph/9911177
  31. Lewis, A., Challinor, A., Hanson, D.: The shape of the CMB lensing bispectrum. JCAP 1103, 018 (2011). arXiv:1101.2234. doi:10.1088/1475-7516/2011/03/018
  32. Lifshitz, E.: On the Gravitational stability of the expanding universe. J. Phys. (USSR) 10, 116 (1946)Google Scholar
  33. Lyth, D.H., Wands, D.: Conserved cosmological perturbations. Phys. Rev. D68, 103515 (2003). arXiv:astro-ph/0306498. doi:10.1103/PhysRevD.68.103515
  34. Malik, K.A., Wands, D.: Cosmological perturbations. Phys. Rep. 475, 1–51 (2009). arXiv:0809.4944. doi:10.1016/j.physrep.2009.03.001
  35. Mather, J.C., Cheng, E.S., Cottingham, D.A., Eplee, R.E., Fixsen, D.J., et al.: Measurement of the cosmic microwave background spectrum by the COBE FIRAS instrument. Astrophys.J. 420, 439–444 (1994). doi:10.1086/173574 ADSCrossRefGoogle Scholar
  36. Mollerach, S., Harari, D., Matarrese, S.: CMB polarization from secondary vector and tensor modes. Phys. Rev. D69, 063002 (2004). arXiv:astro-ph/0310711. doi:10.1103/PhysRevD.69.063002
  37. Mukhanov, V.: Physical foundations of cosmology. Cambridge university press, Cambridge (2005)CrossRefzbMATHGoogle Scholar
  38. Mukhanov, V.F., Feldman, H.A., Brandenberger, R.H.: Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions. Phys. Rep. 215, 203–333 (1992). doi:10.1016/0370-1573(92)90044-Z
  39. Peebles, P.J.E.: Principles of physical cosmology. Princeton University Press, Princeton (1993)Google Scholar
  40. Penzias, A.A., Wilson, R.W.: A measurement of excess antenna temperature at 4080-Mc/s. Astrophys.J. 142, 419–421 (1965). doi:10.1086/148307 ADSCrossRefGoogle Scholar
  41. Pettinari, G.W., Fidler, C., Crittenden, R., Koyama, K., Wands, D.: The intrinsic bispectrum of the cosmic microwave background. JCAP 1304, 003 (2013). arXiv:1302.0832. doi:10.1088/1475-7516/2013/04/003
  42. Pettinari, G.W., Fidler, C., Crittenden, R., Koyama, K., Lewis, A., et al.: Impact of polarization on the intrinsic cosmic microwave background bispectrum. Phys. Rev. D90 (10), 103010 (2014). arXiv:1406.2981. doi:10.1103/PhysRevD.90.103010
  43. Pitrou, C.: The tight-coupling approximation for baryon acoustic oscillations. Phys. Lett. B698, 1–5 (2011). arXiv:1012.0546. doi:10.1016/j.physletb.2011.02.058.
  44. Pitrou, C., Bernardeau, F., Uzan, J.-P.: The y-sky: diffuse spectral distortions of the cosmic microwave background. JCAP 1007, 019 (2010). arXiv:0912.3655. doi:10.1088/1475-7516/2010/07/019
  45. Robertson, H.P.: Kinematics and world-structure. Astrophys. J. 82, 284–301 (1935). doi:10.1086/143681 ADSCrossRefzbMATHGoogle Scholar
  46. Sachs, R.K., Wolfe, A.M.: Perturbations of a cosmological model and angular variations of the microwave background. Astrophys. J. 147, 73–90 (1967). doi:10.1007/s10714-007-0448-9 ADSCrossRefGoogle Scholar
  47. Seljak, U., Zaldarriaga, M.: Direct signature of evolving gravitational potential from cosmic microwave background. Phys. Rev. D60, 043504 (1999). arXiv:astro-ph/9811123. doi:10.1103/PhysRevD.60.043504
  48. Smoot, G.F., Bennett, C.L., Kogut, A., Wright, E.L., Aymon, J., et al.: Structure in the COBE differential microwave radiometer first year maps. Astrophys.J. 396, L1–L5 (1992). doi:10.1086/186504 ADSCrossRefGoogle Scholar
  49. Su, S.C., Lim, E.A., Shellard, E.P.S.: Cosmic microwave background bispectrum from nonlinear effects during recombination. Phys. Rev. D90 (2), 023004 (2014). doi:10.1103/PhysRevD.90.023004 ADSGoogle Scholar
  50. Sunyaev, R.A., Zeldovich, Ya.B.: Small scale fluctuations of relic radiation. Astrophys. Space Sci. 7, 3–19 (1970)Google Scholar
  51. Wands, D.: Local non-Gaussianity from inflation. Class. Quant. Grav. 27, 124002 (2010). arXiv:1004.0818. doi:10.1088/0264-9381/27/12/124002
  52. Wands, D., Malik, K.A., Lyth, D.H., Liddle, A.R.: A new approach to the evolution of cosmological perturbations on large scales. Phys. Rev. D62, 043527 (2000). arXiv:astro-ph/0003278. doi:10.1103/PhysRevD.62.043527
  53. Weinberg, S.: Cosmology. Oxford University Press, Oxford (2008)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • David Wands
    • 1
  • Oliver F. Piattella
    • 2
  • Luciano Casarini
    • 2
  1. 1.Institute of Cosmology and GravitationUniversity of PortsmouthPortsmouthUK
  2. 2.Departamento de FísicaUniversidade Federal do Espírito SantoVitória, Espírito SantoBrazil

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