Mathematics – Logic
Scientific paper
Apr 1989
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989stin...8926791f&link_type=abstract
Unknown
Mathematics
Logic
Approximation, Big Bang Cosmology, Electromagnetic Radiation, Gravitational Fields, Inhomogeneity, Red Shift, Universe, Bimetric Theories, Einstein Equations, Metric Space, Relativity
Scientific paper
The propagation of light rays in a clumpy universe constructed by cosmological version of the post-Newtonian approximation was investigated. It is shown that linear approximation to the propagation equations is valid in the region where zeta is approximately less than 1 even if the density contrast is much larger than unity. Based on a gerneral order-of-magnitude statistical consideration, it is argued that the linear approximation is still valid where zeta is approximately greater than 1. A general formula for the distance-redshift relation in a clumpy universe is given. An explicit expression is derived for a simplified situation in which the effect of the gravitational potential of inhomogeneities dominates. In the light of the derived relation, the validity of the Dyer-Roeder distance is discussed. Also, statistical properties of light rays are investigated for a simple model of an inhomogeneous universe. The result of this example supports the validity of the linear approximation.
Futamase Toshifumi
Sasaki Misao
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