The Sachs-Wolfe effect in some anisotropic models

Paulo Aguiar, Paulo Crawford1


It is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the last scattering surface produce anisotropies on large angular scales (larger than θ > 2°) which do not differ from the ones produced in Friedmann-Lemaitre-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by the same expression as the one given for FLRW models. More precisely, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, provided the anisotropy of the overall expansion is small. This conclusion is in agreement with previous work on the same anisotropic models where we found that they may go through an "˜isotropization" process up to the pointthat the observations are unable to distinguish them from the standard FLRW model, if the Hubble parameters along the orthogonal directions are assumed to be approximately equal at the present epoch. Here we assumed upper bounds on the present values of anisotropy parameters imposed by COBE observations.


  1. J. Ehlers, P. Geren, and R. K. Sachs, J. Math. Phys. 9, 1344 (1968).
  2. U. S. Nilsson et al., Astrophys. J. 522, L1 (1999).
  3. W. R. Stoeger, R. Maartens, and G. F. R. Ellis, Astrophys. J. 443, 1 (1995).
  4. W. C. Lim et al., Class. Quantum Grav. 18, 5583 (2001).
  5. A. Henriques, Astroph. Space Sci. 235, 129 (1996).
  6. P. Aguiar and P. Crawford, Phys. Rev. D 62, 123511 (2000).
  7. P. Aguiar and P. Crawford, "Numerical Cumputation of an Integral"
  8. A. A. Penzias and R. W. Wilson, Astrophys. J. 142, 419 (1965).
  9. G. F. Smoot, Astrophys. J. 396, L1 (1992).
  10. P. Coles and F. Lucchin, Cosmology-The Origin and Evolution of Cosmic Structure (Wiley, Chichester, England 1995), p. 185.
  11. J. C. Mather et al., Astrophys. J. 420, 439 (1994).
  12. R. B. Partridge, Class. Quant. Grav. 11, A153 (1994).
  13. R. B. Partridge, Rep. Prog. Phys. 51, 647 (1988).
  14. R. K. Sachs and A. M. Wolfe, Astrophys. J. 147, 73 (1967).
  15. C. B. Collins and S. W. Hawking, Mon. Not. Astron. Soc. 162, 307 (1973).
  16. M. White et al., Ann. Rev. Astron. Astrophys. 32, 319 (1994).
  17. A. R. Liddle and D. H. Lyth, Cosmological Inflation and Large-Scale Structure (Cambridge University Press, Cambridge, 2000).
  18. V. F. Mukhanov et al., Phys. Rep. 215, 203 (1992).
  19. W. Hu, PhD Thesis (Univ. of California, Berkeley, 1995), Chapter 4.
  20. S. Perlmutter et al., Nature 391, 51 (1998).
  21. A. G. Riess et al., Astron. J. 116, 1009 (1998).
  22. E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, 1990), Chapter 9.2.
  25. E. Martinez-Gonzalez and J. L. Sanz, Astron. Astrophys. 300, 346 (1995).
  26. R. Maartens et al., Astron. Astrophys. 309, L7 (1996).
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