Astrophysics and Space Science

, Volume 7, Issue 1, pp 3–19

Small-scale fluctuations of relic radiation

  • R. A. Sunyaev
  • Ya. B. Zeldovich

DOI: 10.1007/BF00653471

Cite this article as:
Sunyaev, R.A. & Zeldovich, Y.B. Astrophys Space Sci (1970) 7: 3. doi:10.1007/BF00653471


Perturbations of the matter density in a homogeneous and isotropic cosmological model which leads to the formation of galaxies should, at later stages of evolution, cause spatial fluctuations of relic radiation. Silk assumed that an adiabatic connection existed between the density perturbations at the moment of recombination of the initial plasma and fluctuations of the observed temperature of radiation δT/Tϱm/3ϱm. It is shown in this article that such a simple connection is not applicable due to:
  1. (1)

    The long time of recombination;

  2. (2)

    The fact that when regions withM<1015M become transparent for radiation, the optical depth to the observer is still large due to Thompson scattering;

  3. (3)

    The spasmodic increase of δϱm/ϱm in recombination.


As a result the expected temperature fluctuations of relic radiation should be smaller than adiabatic fluctuations. In this article the value of δT/T arising from scattering of radiation on moving electrons is calculated; the velocity field is generated by adiabatic or entropy density perturbations. Fluctuations of the relic radiation due to secondary heating of the intergalactic gas are also estimated. A detailed investigation of the spectrum of fluctuations may, in principle, lead to an understanding of the nature of initial density perturbations since a distinct periodic dependence of the spectral density of perturbations on wavelength (mass) is peculiar to adiabatic perturbations. Practical observations are quite difficult due to the smallness of the effects and the presence of fluctuations connected with discrete sources of radio emission.

Copyright information

© D. Reidel Publishing Company 1970

Authors and Affiliations

  • R. A. Sunyaev
    • 1
  • Ya. B. Zeldovich
    • 1
  1. 1.Institute of Applied MathematicsAcademy of Sciences of the U.S.S.R.MoscowUSSR

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