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The Sachs-Wolfe effect, named after Rainer Kurt Sachs and Arthur Michael Wolfe, is a property of the cosmic microwave background radiation (CMB), in which photons from the CMB are gravitationally redshifted, causing the CMB spectrum to appear uneven. This effect is the predominant source of fluctuations in the CMB for angular scales above about ten degrees.

Non-Integrated Sachs-Wolfe Effect

The non-integrated Sachs-Wolfe effect is caused by gravitational redshift occurring at the surface of last scattering. The effect is not constant across the sky due to differences in the matter/energy density at the time of last scattering.

Integrated Sachs-Wolfe Effect

The Integrated Sachs-Wolfe effect is also caused by gravitational redshift, however here it occurs between the surface of last scattering and the Earth, so it is not a fundamental part of the CMB.

There are two main contributions to the integrated effect. The first occurs shortly after photons leave the last scattering surface, and is due to the evolution of the potential wells as the universe changes from being dominated by radiation to being dominated by matter. The second, sometimes called the 'late-time integrated Sachs Wolfe effect', arises much later as the evolution starts to feel the effect of the cosmological constant (or, more generally, dark energy), or curvature of the Universe if it is not flat. The latter effect has an observational signature in the amplitude of the large scale perturbations of the cosmic microwave background and their correlation with large scale structures in the universe.


* Sachs, R. K.; Wolfe, A. M. (1967). "Perturbations of a cosmological model and angular variations of the cosmic microwave background". Astrophysical Journal 147 (73).​


* Sam LaRoque, The Integrated Sachs-Wolfe Effect. University of Chicago, IL.
* Aguiar, Paulo, and Paulo Crawford, Sachs-Wolfe effect in some anisotropic models. (PDF format)
* White, Martin, and Wayne Hu, The Sachs-Wolfe effect. Astronomy and Astrophysics 321, 8­9. 1997. Enrico Fermi Institute, University of Chicago. (PDF format)

* Sachs-Wolfe effect Level 5.

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