Cmb: Anisotropies Due to Non-Linear Clustering

  • E. Martíinez-González
  • J. L. Sanz
Part of the International Astronomical Union/Union Astronomique Internationale book series (IAUS, volume 168)


Most of the studies on the anisotropy expected in the temperature of the cosmic microwave background (CMB) have been based on linear density perturbations. The anisotropics at angular scales ≥ 1° (horizon at recombination) are preserved during the evolution of the universe, whereas for smaller scales new effects can appear, generated during the non-linear phase of matter clustering evolution: i) the Sunyaev-Zeldovich effect due to hot gas in clusters (Scaramella et. al. 1993), ii) the Vishniac effect (Vishniac 1987) due to the coupling between density fluctuations and bulk motions of gas and iii) the integrated gravitational effect (Martíinez-González et. al. 1994) due to time-varyng gravitational potentials. A single potential φ(t, x), satisfying the Poisson equation, is enouph to describe weak gravitational fields associated to non-linear density fluctuations when one considers scales smaller than the horizon and non-relativistic peculiar velocities. The temperature anisotropics, in a flat universe, are given by the expression (Martíinez-González et. al. 1990)


Cosmic Microwave Background Stable Cluster Angular Scale Bulk Motion Flat Universe 
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  4. Vishniac, E. T. (1987), The Astrophysical Journal Vol. no. 322, 597ADSCrossRefGoogle Scholar

Copyright information

© International Astronomical Union 1996

Authors and Affiliations

  • E. Martíinez-González
    • 1
  • J. L. Sanz
    • 1
  1. 1.Dpto. de Fisica ModernaUniversidad de Cantabria and Instituto de Estudios Avanzados, CSIC Universidad de Cantabria Facultad de CienciasSantanderSpain

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