Astron. Astrophys. 323, 305-311 (1997)

5. Conclusion

We have investigated the behavior of the observed CMB temperature anisotropy correlation function in a universe with density inhomogeneities causing a gaussian light deflection field, both correlated with and independent of the perturbations giving rise to the temperature fluctuations. The ratio of the correlated effect to the independent one is of order the cross correlation parameter squared, . While one might expect that the deflection and temperature be strongly coupled, (cf. Eq. 42), this is found not to be true here. In the case of gravitational lensing of photons from the last scattering surface the correlation influence on CMB anisotropies is negligible because one loses the path length "resonance" of the deflections and temperature fluctuations together tracing the gravitational potential field along the entire line of sight. Such a dependence would increase the correlation parameter by a factor of , making the effect significant. Due to the quasistatic nature of the potential along the path, however, this does not give rise to observable temperature fluctuations. Exceptions occur only in localized events such as cluster formation (Rees & Sciama 1968) or hot cluster cores (Sunyaev & Zel'dovich 1970), which do not offer the opportunity for path resonance or gaussian statistics.

Although the correlation of the two density perturbation derived variables considered here can be neglected, the formalism of calculating probability distributions and covariances of gaussian fluctuations is powerful. Insights garnered here into the methods and relations may prove useful in other cosmological applications such as analyzing large scale velocity flows.

© European Southern Observatory (ESO) 1997

Online publication: June 5, 1998

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