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Astron. Astrophys. 319, 729-736 (1997)

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The anisotropy of the cosmic background radiation due to mass clustering in a closed universe *

Daming Chen 1, Guoxuan Song 1 and Yougen Shen 2, 1

1 Shanghai Observatory, Academia Sinica, Shanghai, 200030, China
2 China Center of Advanced Science and Technology (World Laboratory), P. O. Box 8730, Beijing 100080, China

Received 10 June 1996 / Accepted 11 September 1996


We consider the effects on the Cosmic Background Radiation (CBR) of a single, spherically symmetric structure using the Tolman-Bondi solutions in a closed universe. The exact frequency shift of a photon passing through the center of a lump which is located between the last scattering surface and an observer is calculated. An approximate expression of the frequency shift [FORMULA] to the first order of [FORMULA] (the density contrast) is given. We find that there are several redshifts of the perturbing lump where the net frequency shift is zero. With increasing [FORMULA], the first positions of zero frequency shift move toward lower redshift; the larger the value of [FORMULA], the further they move. At the vicinity of the last scattering surface, where the universe is close to flat, the frequency shift will always be the same as that for a flat universe.

Key words: cosmic microwave background – cosmology: theory – large-scale structure of the universe

* Supported by the National Natural Science Foundation of China and the Young Astronomer Laboratory of Shanghai Observatory

Send offprint requests to: Daming Chen


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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998