Skip to main content
SpringerLink
Log in

The Cosmic Microwave Background Radiation

  • Chapter
  • First Online:
Galaxy Formation

Part of the book series: Astronomy and Astrophysics Library ((AAL))

  • 899 Accesses

Summary

The Cosmic Microwave Background Radiation (CMB) provides a wealth of precision cosmological data. The properties of the intensity and polarisation fluctuations are analysed in some detail from a physical point of view. The analysis of the observations requires an understanding of the ionisation state of the primordial gas through the crucial epoch of recombination at z ∼ 1050 and the later reionisation epoch. The many physical processes contributing to the predicted power-spectrum are discussed, involving all the cosmological physics developed in earlier chapters. The remarkable result of these analyses is that the properties of the power spectra of galaxies and the CMB are consistent with what has become the standard ΛCDM model with flat spatial geometry Ωκ = 0, Ω0 ≈ 0.3, ΩB ≈ 0.05, ΩΛ ≈ 0.7, h ≈ 0.68. Key cosmological parameters have been determined to about 3% or better. Remarkably, the whole analysis, including the determination of the cosmological parameters can be carried out entirely from analysis of the CMB data-sets. The values found are consistent with those determined by independent approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The advanced version of the Cosmology Calculator developed by Dr. Edward Wright is a useful tool for understanding the effects of changing the cosmological parameters upon distances and times. (see https://ned.ipac.caltech.edu/help/cosmology_calc.html).

  2. 2.

    https://camb.readthedocs.io/en/latest/.

  3. 3.

    A detailed discussion of the long and complex story of the determination of the properties of the CMB is contained in the book Finding the Big Bang by Peebles et al. (2009) which was published before the Planck mission was launched. Figures 5.9 to 5.18 of that book provide an excellent overview of the history of the searches for fluctuations in the CMB. Partridge brings the story up to date in his essay The Cosmic Background Radiation (Partridge, 2019).

  4. 4.

    Hu writes the derivatives with respect to conformal time rather than cosmic time, but this is not important since we have removed the expansion of the Universe from our illustrative calculation.

  5. 5.

    The acronyms stand for: CBI = Cosmic Background Imager; CAPMAP = Cosmic Anisotropy Polarization Mapper; BOOMERanG = Balloon Observations Of Millimetric Extragalactic Radiation ANisotropy and Geophysics.

  6. 6.

    For a simple introduction to gravitational radiation, see the review by Schutz (2001).

References

  • Abbott, T. M. C., Aguena, M., Alarcon, A., et al. (2022a). Dark energy survey year 3 results: Cosmological constraints from galaxy clustering and weak lensing. Physical Review D, 105(2), 023520. https://doi.org/10.1103/PhysRevD.105.023520

    Article  ADS  Google Scholar 

  • Abbott, T. M. C., Aguena, M., Allam, S., et al. (2022b). Dark energy survey year 3 results: A 2.7% measurement of baryon acoustic oscillation distance scale at redshift 0.835. Physical Review D, 105(4), 043512. https://doi.org/10.1103/PhysRevD.105.043512

  • Barkats, D., Bischoff, C., Farese, P., et al. (2005). First measurements of the polarization of the Cosmic Microwave Background radiation at small angular scales from CAPMAP. The Astrophysical Journal Letters, 619, L127–L130.

    Article  ADS  Google Scholar 

  • Baumann, D. (2022). Cosmology. Cambridge University Press.

    Book  MATH  Google Scholar 

  • Bennett, C. L., Banday, A. J., Gorski, K. M., et al. (1996). Four-year COBE DMR Cosmic Microwave Background observations: Maps and basic results. The Astrophysical Journal, 464, L1–L4.

    Article  ADS  Google Scholar 

  • Bennett, C., Halpern, M., Hinshaw, G., et al. (2003). First-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Preliminary maps and basic results. The Astrophysical Journal Supplement Series, 148, 1–27.

    Article  ADS  Google Scholar 

  • Bourne, N., Dunne, L., Maddox, S. J., et al. (2016). The Herschel-ATLAS data release 1. II: Multi-wavelength counterparts to submillimetre sources. Monthly Notices of the Royal Astronomical Society, 462(2), 1714–1734. https://doi.org/10.1093/mnras/stw1654

    Article  ADS  Google Scholar 

  • Bracewell, R. (1986). The Fourier transform and its applications. McGraw–Hill Book Company.

    Google Scholar 

  • Carlstrom, J. E., Joy, M. K., Grego, L., et al. (2000). Imaging the Sunyaev-Zel’dovich effect. In L. Bergström, P. Carlson, & C. Fransson (Eds.), Particle physics and the Universe: Proceedings of nobel symposium 198 (pp. 148–155). Physica Scripta.

    Google Scholar 

  • Challinor, A. (2005). Cosmic Microwave Background anisotropies. In K. Tamvakis (Ed.) Lecture notes in physics: The physics of the early Universe (Vol. 653, pp. 71–103). Springer Verlag.

    Google Scholar 

  • Chluba, J., & Sunyaev, R. A. (2006). Induced two-photon decay of the 2s level and the rate of cosmological hydrogen recombination. Astronomy & Astrophysics, 446, 39–42. https://doi.org/10.1051/0004-6361:20053988

    Article  ADS  Google Scholar 

  • Crittenden, R., Bond, R., Davis, R. L., et al. (1993). Imprint of gravitational waves on the Cosmic Microwave Background. Physical Review Letters, 71, 324–327.

    Article  ADS  Google Scholar 

  • Das, S., Louis, T., Nolta, M., et al. (2014). The Atacama Cosmology Telescope: Temperature and gravitational lensing power spectrum measurements from three seasons of data. Journal of Cosmology and Astroparticle Physics, 2014(4), 014. https://doi.org/10.1088/1475-7516/2014/04/014

    Article  Google Scholar 

  • Davis, R. L., Hodges, H. M., Smoot, G. F., et al. (1992). Cosmic Microwave Background probes models of inflation. Physical Review Letters, 69, 1856–1859.

    Article  ADS  Google Scholar 

  • de Bernardis, P., Ade, P. A. R., Bock, J. J., et al. (2000). A flat Universe from high-resolution maps of the Cosmic Microwave Background radiation. Nature, 404, 955–959.

    Article  ADS  Google Scholar 

  • Dodelson, S. (2003). Modern cosmology. Academic Press. Second edition with F. Schmidt, 2020.

    Google Scholar 

  • Dodelson, S., Gates, E. I., & Turner, M. S. (1996). Cold dark matter. Science, 274, 69–75.

    Article  ADS  Google Scholar 

  • Efstathiou, G. (1988). Effects of reionization on Microwave Background anisotropies. In V. Rubin & G. Coyne (Eds.), Large-scale motions in the Universe (pp. 299–319). Princeton University Press.

    Google Scholar 

  • Efstathiou, G. (1990). Cosmological perturbations. In J. A. Peacock, A. F. Heavens, & A. T. Davies (Eds.), Physics of the early Universe (pp. 361–463). SUSSP Publications.

    Google Scholar 

  • Hanany, S., Ade, P., Balbi, A., et al. (2000). MAXIMA-1: A measurement of the Cosmic Microwave Background anisotropy on angular scales of 10’-5°. The Astrophysical Journal, 545(1), L5–L9. https://doi.org/10.1086/317322

    Article  ADS  Google Scholar 

  • Hand, N., Addison, G. E., Aubourg, E., et al. (2012). Evidence of galaxy cluster motions with the kinematic Sunyaev-Zel’dovich effect. Physical Review Letters, 109(4), 041101. https://doi.org/10.1103/PhysRevLett.109.041101

    Article  ADS  Google Scholar 

  • Hinshaw, G., Nolta, M. R., Bennett, C. L., et al. (2007). Three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Temperature analysis. The Astrophysical Journal Supplement Series, 170, 288–334.

    Article  ADS  Google Scholar 

  • Hu, W. (1996). Concepts in CMB anisotropy formation. In E. Martinez-Gonzales & J. L. Sanz (Eds.), The Universe at high-z, Large-scale structure and the Cosmic Microwave Background (pp. 207–240). Springer-Verlag.

    Google Scholar 

  • Hu, W., & Dodelson, S. (2002). Cosmic Microwave Background anisotropies. Annual Review of Astronomy and Astrophysics, 40, 171–216.

    Article  ADS  Google Scholar 

  • Hu, W., & Okamoto, T. (2002). Mass reconstruction with Cosmic Microwave Background polarization. The Astrophysical Journal, 574, 566–574.

    Article  ADS  Google Scholar 

  • Hu, W., & Sugiyama, N. (1995). Anisotropies in the Cosmic Microwave Background: an analytic approach. The Astrophysical Journal, 444, 489–506.

    Article  ADS  Google Scholar 

  • Hu, W., & White, M. (1997). A CMB polarization primer. New Astronomy, 2, 323–344.

    Article  ADS  Google Scholar 

  • Hu, W., Sugiyama, N., & Silk, J. (1997). The physics of Microwave Background anisotropies. Nature, 386, 37–43.

    Article  ADS  Google Scholar 

  • Jones, B. J. T., & Wyse, R. F. G. (1985). The ionisation of the primeval plasma at the time of recombination. Astronomy & Astrophysics, 149, 144–150.

    ADS  Google Scholar 

  • Kaiser, N. (1992). Weak gravitational lensing of distant galaxies. The Astrophysical Journal, 388, 272–286.

    Article  ADS  Google Scholar 

  • Kibble, T. W. B. (1976). Topology of cosmic domains and strings. Journal of Physics A: Mathematical and General, 9, 1387–1398.

    Article  ADS  MATH  Google Scholar 

  • Kogut, A., Banday, A. J., Bennett, C. L., et al. (1996). Tests for non-Gaussian statistics in the DMR four-year sky maps. The Astrophysical Journal, 464, L29–L33.

    Article  ADS  Google Scholar 

  • Kovac, J. M., Leitch, E. M., Pryke, C., et al. (2002). Detection of polarization in the Cosmic Microwave Background using DASI. Nature, 420, 772–787.

    Article  ADS  Google Scholar 

  • Lahav, O., Calder, L., Julian Mayers, J., & Frieman, J. (2020). The dark energy survey: The story of a cosmological experiment. World Scientific Publishing Europe Ltd.

    Book  Google Scholar 

  • Leitch, E. M., Kovac, J. M., Pryke, C., et al. (2002). Measurement of polarization with the degree angular scale interferometer. Nature, 420, 763–771.

    Article  ADS  Google Scholar 

  • Lewis, A., & Challinor, A. (2006). Weak gravitational lensing of the CMB. Physics Reports, 429(1), 1–65. https://doi.org/10.1016/j.physrep.2006.03.002

    Article  ADS  Google Scholar 

  • Lewis, A., Challinor, A., & Hanson, D. (2011). The shape of the CMB lensing bispectrum. Journal of Cosmology and Astroparticle Physics, 2011(03), 018.

    Article  Google Scholar 

  • Lineweaver, C. H. (2005). Inflation and the Cosmic Microwave Background. In M. Colless (Ed.),The new cosmology (pp. 31–65). World Scientific.

    Google Scholar 

  • Matthews, J., & Walker, R. L. (1973). Mathematical methods of physics. W.A. Benjamin.

    Google Scholar 

  • Montroy, T. E., Ade, P. A. R., Bock, J. J., et al. (2006). A measurement of the CMB 〈EE〉 spectrum from the 2003 flight of BOOMERANG. The Astrophysical Journal, 647, 813–822.

    Article  ADS  Google Scholar 

  • Padmanabhan, T. (1993). Structure formation in the Universe. Cambridge University Press.

    Google Scholar 

  • Padmanabhan, T. (1996). Cosmology and astrophysics through problems (pp. 437–440). Cambridge University Press.

    Google Scholar 

  • Page, L., Hinshaw, G., Komatsu, E., et al. (2007). Three-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: Polarization analysis. The Astrophysical Journal Supplement Series, 170, 335–376.

    Article  ADS  Google Scholar 

  • Partridge, R. B. (2019). The Cosmic Microwave Background: from discovery to precision cosmology. In H. Kragh & M. Longair (Eds.), The Oxford handbook of the history of modern cosmology (pp. 292–345). Oxford University Press.

    Google Scholar 

  • Peacock, J. (1999). Cosmological physics. Cambridge University Press.

    MATH  Google Scholar 

  • Peacock, J. A., & Dodds, S. J. (1994). Reconstructing the linear power spectrum of cosmological mass fluctuations. Monthly Notices of the Royal Astronomical Society, 267, 1020–1034.

    Article  ADS  Google Scholar 

  • Peebles, P. J. E. (1968). Recombination of the primeval plasma. The Astrophysical Journal, 153, 1–11.

    Article  ADS  Google Scholar 

  • Peebles, P. J. E. (1980). The large-scale structure of the Universe. Princeton University Press.

    MATH  Google Scholar 

  • Peebles, P. J. E. (1993). Principles of physical cosmology. Princeton University Press.

    MATH  Google Scholar 

  • Peebles, P. J. E., & Yu, J. T. (1970). Primeval adiabatic perturbation in an expanding Universe. The Astrophysical Journal, 162, 815–836.

    Article  ADS  Google Scholar 

  • Peebles, P. J. E., Page, Lyman A., J., & Partridge, R. B. (2009). Finding the Big Bang. Cambridge University Press.

    Google Scholar 

  • Planck Collaboration, Ade, P. A. R., Aghanim, N., Alves, M. I. R., et al. (2014). Planck 2013 results. I: Overview of products and scientific results. Astronomy & Astrophysics, 571, A1. https://doi.org/10.1051/0004-6361/201321529

  • Planck Collaboration, Ade, P. A. R., Aghanim, N., Argüeso, F., et al. (2016a). Planck 2015 results. XXVI: The second Planck catalogue of compact sources. Astronomy & Astrophysics, 594, A26. https://doi.org/10.1051/0004-6361/201526914

  • Planck Collaboration, Aghanim, N., Arnaud, M., et al. (2016b). Planck 2015 results. XXII: A map of the thermal Sunyaev-Zeldovich effect. Astronomy & Astrophysics, 594, A22. https://doi.org/10.1051/0004-6361/201525826

  • Planck Collaboration, Aghanim, N., Akrami, Y., et al. (2018). Planck intermediate results. LIII: Detection of velocity dispersion from the kinetic Sunyaev-Zeldovich effect. Astronomy & Astrophysics, 617, A48. https://doi.org/10.1051/0004-6361/201731489

  • Planck Collaboration, Aghanim, N., Akrami, Y., Arroja, F., et al. (2020a). Planck 2018 results. I: Overview and the cosmological legacy of Planck. Astronomy & Astrophysics, 641, A1. https://doi.org/10.1051/0004-6361/201833880

  • Planck Collaboration, Aghanim, N., Akrami, Y., Ashdown, M., et al. (2020b). Planck 2018 results. V: CMB power spectra and likelihoods. Astronomy & Astrophysics, 641, A5. https://doi.org/10.1051/0004-6361/201936386

  • Planck Collaboration, Aghanim, N., Akrami, Y., Ashdown, M., et al. (2020c). Planck 2018 results. VI: Cosmological parameters, Astronomy & Astrophysics, 641, A6. https://doi.org/10.1051/0004-6361/201833910

  • Planck Collaboration, Aghanim, N., Akrami, Y., Ashdown, M., et al. (2020d). Planck 2018 results. VIII: Gravitational lensing. Astronomy & Astrophysics, 641, A8. https://doi.org/10.1051/0004-6361/201833886

  • Planck Collaboration, Akrami, Y., Arroja, F., Ashdown, M., et al. (2020e). Planck 2018 results. IX: Constraints on primordial non-Gaussianity. Astronomy & Astrophysics, 641, A9. https://doi.org/10.1051/0004-6361/201935891

  • Readhead, A. C. S., Mason, B. S., Contaldi, C. R., et al. (2004). Extended mosaic observations with the cosmic background imager. The Astrophysical Journal, 609, 498–512.

    Article  ADS  Google Scholar 

  • Rees, M. J., & Sciama, D. W. (1968). Large-scale density inhomogeneities in the Universe. Nature, 217, 511–516.

    Article  ADS  Google Scholar 

  • Refregier, A. (2003). Weak gravitational lensing by large-scale structure. Annual Review of Astronomy and Astrophysics, 41, 645–668.

    Article  ADS  Google Scholar 

  • Sachs, R., & Wolfe, A. (1967). Perturbations of a cosmological model and angular variations in the Microwave Background. The Astrophysical Journal, 147, 73–90.

    Article  ADS  Google Scholar 

  • Schutz, B. (2001). Gravitational radiation. In P. Murdin (Ed.), Encyclopaedia of astronomy and astrophysics (Vol. 2, pp. 1030–1042). Institute of Physics Publishing/Nature Publishing Group.

    Google Scholar 

  • Scott, D., & Smoot, G. (2020). Cosmic Microwave Background. In P. A. Zyla et al. (Particle Data Group) (Eds.), 2020 Review of particle physics. Progress of theoretical and experimental physics 2020 (pp. 499–509, 083C01). This volume includes updates to material published in 2021.

    Google Scholar 

  • Seager, S., Sasselov, D. D., & Scott, D. (2000). How exactly did the Universe become neutral? The Astrophysical Journal Supplement Series, 128, 407–430.

    Article  ADS  Google Scholar 

  • Starobinsky, A. A. (1985). Cosmic background anisotropy induced by isotropic flat-spectrum gravitational-wave perturbations. Soviet Astronomy Letters, 11, 133–137. In Russian: Pis’ma v Astronomicheskii Zhurnal, 11, 323–330 (1985).

    Google Scholar 

  • Story, K. T., Reichardt, C. L., Hou, Z., et al. (2013). A measurement of the Cosmic Microwave Background damping tail from the 2500-square-degree SPT-SZ survey. The Astrophysical Journal, 779(1), 86. https://doi.org/10.1088/0004-637X/779/1/86

    Article  ADS  Google Scholar 

  • Subramanian, K. (2005). The physics of CMBR anisotropies. Current Science, 88, 1068–1087.

    Google Scholar 

  • Sunyaev, R., & Zeldovich, Y. (1970a). Small-scale fluctuations of relic radiation. Astrophysics and Space Science, 7, 3–19.

    Article  ADS  Google Scholar 

  • Sunyaev, R. A., & Zeldovich, Y. B. (1980b). The velocity of clusters of galaxies relative to the Microwave Background: The possibility of its measurement. Monthly Notices of the Royal Astronomical Society, 190, 413–420.

    Article  ADS  Google Scholar 

  • Trushkin, S. A. (2003). Radio spectra of the WMAP catalog sources. Bulletin of the Special Astrophysical Observatory, 55, 90–132.

    ADS  Google Scholar 

  • Turner, M. (1997). Inflationary cosmology. In B. J. T. Jones & D. Markovic (Eds.), Relativistic Astrophysics (pp. 83–102). Cambridge University Press.

    Google Scholar 

  • Turok, N. (1989). Global texture as the origin of cosmic structure. Physical Review Letters, 63, 2625–2628.

    Article  ADS  Google Scholar 

  • Valiante, E., Smith, M. W. L., Eales, S., et al. (2016). The Herschel-ATLAS data release 1. I: Maps, catalogues and number counts. Monthly Notices of the Royal Astronomical Society, 462(3), 3146–3179. https://doi.org/10.1093/mnras/stw1806

    Article  ADS  Google Scholar 

  • Vishniac, E. T. (1987). Reionization and small-scale fluctuations in the Microwave Background. The Astrophysical Journal, 322, 597–604.

    Article  ADS  Google Scholar 

  • White, M., Scott, D., and Silk, J., (1994). Annual Review of Astronomy and Astronphysics, 32, 319–370.

    Article  ADS  Google Scholar 

  • Will, C. (2018). Theory and experiment in gravitational physics (2nd ed.). Cambridge University Press.

    Book  MATH  Google Scholar 

  • Zaldarriaga, M. (1997). Polarization of the Microwave Background in reionized models. Physical Review D, 55, 1822–1829.

    Article  ADS  Google Scholar 

  • Zaldarriaga, M. (2004). The polarization of the Cosmic Microwave Background. In W. L. Freedman (Ed.), Measuring and modeling the Universe (pp. 309–329). Cambridge University Press.

    Google Scholar 

  • Zeldovich, Y. B., Kurt, D., & Sunyaev, R. A. (1968). Recombination of hydrogen in the hot model of the Universe. Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 55, 278–286. Translation: Soviet Physics - JETP, 28, 146–150 (1969).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Cambridge, Cambridge, UK

    Malcolm S. Longair

Authors
  1. Malcolm S. Longair
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2023 The Author(s), under exclusive license to Springer-Verlag GmbH, DE, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Longair, M.S. (2023). The Cosmic Microwave Background Radiation. In: Galaxy Formation. Astronomy and Astrophysics Library. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-65891-8_15

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-65891-8_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-65890-1

  • Online ISBN: 978-3-662-65891-8

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation