Sachs-Wolfe effect

The Sachs-Wolfe effect [ [http://adsabs.harvard.edu/abs/1967ApJ...147...73S "Perturbations of a Cosmological Model and Angular Variations of the Microwave Background"] Sachs R.K., & Wolfe A.M., 1967, ApJ, 147, 73] , 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 (ISW) is also caused by gravitational redshift, however it occurs between the surface of last scattering and the Earth, so it is not part of the primordial CMB. It occurs when the Universe is dominated in its density by something other than matter. If the Universe is dominated by matter, then large-scale gravitational potential wells and hills do not evolve significantly. If the Universe is dominated by radiation, or by dark energy, though, those potentials do evolve, subtly changing the energy of photons passing through them.

There are two contributions to the ISW effect. The "early-time" ISW occurs immediately after the (non-integrated) Sachs-Wolfe effect produces the primordial CMB, as photons course through density fluctuations while there is still enough radiation around to affect the Universe's expansion. Although it is physically the same as the late-time ISW, for observational purposes it is usually lumped in with the primordial CMB, since the matter fluctuations that cause it are in practice undetectable.

Late-time Integrated Sachs-Wolfe Effect

The "late-time" ISW effect arises quite recently in cosmic history, as dark energy, or the cosmological constant, starts to govern the Universe's expansion. Unfortunately, the nomenclature is a bit confusing. Often, "late-time ISW" implicitly refers to the late-time ISW effect to linear/first order in density perturbations. This linear part of the effect entirely vanishes in a flat universe with only matter, but dominates over the higher-order part of the effect in a universe with dark energy. The full nonlinear (linear + higher-order) late-time ISW effect, especially in the case of individual voids and clusters, is sometimes known as the Rees-Sciama ["Large-scale Density Inhomogeneities in the Universe", Rees, M.J. & Sciama, D.W., Nature, 217, 511] effect, since Martin Rees and Dennis Sciama elucidated the following physical picture.

Accelerated expansion due to dark energy causes even strong large-scale potential wells and hills to decay over the time it takes a photon to travel through them. A photon gets a kick of energy going into a potential well (a supercluster), and it keeps some of that energy after it exits, after the well has been stretched out and shallowed. Similarly, a photon has to expend energy entering a supervoid, but will not get all of it back upon exiting the slightly squashed potential hill.

A signature of the late-time ISW is a non-zero cross-correlation function between the galaxy density (the number of galaxies per square degree) and the temperature of the CMB [ [http://arxiv.org/abs/astro-ph/9510072 "Looking for Lambda with the Rees-Sciama Effect"] , Crittenden R.G., & Turok N., 1996, Phys. Rev. Lett., 76, 575] , because superclusters gently heat photons, while supervoids gently cool them. This correlation has been detected at moderate to high significance [ [http://arxiv.org/abs/astro-ph/0307335 "Physical Evidence for Dark Energy"] , Scranton et al., 2003] [ [http://lanl.arxiv.org/abs/0801.0642 "Correlation of CMB with large-scale structure: I. ISW Tomography and Cosmological Implications"] , Ho et al., 2008, Phys Rev. D, submitted] [ [http://arxiv.org/abs/0801.4380 "Combined analysis of the integrated Sachs-Wolfe effect and cosmological implications"] , Giannantonio et al., 2008, Phys. Rev. D, in press] .

In May 2008, Granett, Neyrinck & Szapudi [ [http://arxiv.org/abs/0805.3695 "An Imprint of Super-Structures on the Microwave Background due to the Integrated Sachs-Wolfe Effect"] , Granett, Neyrinck & Szapudi, 2008, ApJL, submitted] showed that the late-time ISW can be pinned to discrete supervoids and superclusters identified in the SDSS Luminous Red Galaxy catalog. Their ISW detection is arguably the clearest to date, producing an image of the mean effect supervoids and superclusters have on the CMB.

References

External links

* Sam LaRoque, " [http://astro.uchicago.edu/~laroque/ISW.html The Integrated Sachs-Wolfe Effect] ". University of Chicago, IL.
* Aguiar, Paulo, and Paulo Crawford, " [http://cosmo.fis.fc.ul.pt/~crawford/papers/swf_cqg.pdf Sachs-Wolfe effect in some anisotropic models] ". (PDF format)
* White, Martin, and Wayne Hu, " [http://background.uchicago.edu/~whu/Papers/sw.pdf The Sachs-Wolfe effect] ". Astronomy and Astrophysics 321, 8­9. 1997. Enrico Fermi Institute, University of Chicago. (PDF format)
* [http://nedwww.ipac.caltech.edu/level5/Glossary/Essay_sachswolfe.html Sachs-Wolfe effect] Level 5.
* [http://www.ifa.hawaii.edu/cosmowave/supervoids "Dark Energy and the Imprint of Super-Structures on the Microwave Background"] , a webpage by Granett, Neyrinck & Szapudi.