Critical Lines in Gravitational Lenses and the Determination of Cosmological Parameters

Details Critical Lines in Gravitational Lenses and the Determination of Cosmological Parameters Critical Lines in Gravitational Lenses and the Determination of Cosmological Parameters

1996-11-14

arxiv.org/abs/astro-ph/9611110v1

Astronomy and Astrophysics

Astrophysics

16 pages, LaTeX(aaspp4), 11 postscript figures included; submitted to The Astrophysical Journal

Scientific paper

10.1086/304452

We investigate the cosmological test recently proposed by B. Fort, Y. Mellier and M. Dantel-Fort (FMD), where the observed location of the critical line in gravitational lensing is used to determine the cosmological parameters, $\Omega$ and $\lambda$. Applying this method to the cluster of galaxies Cl0024+1654, FMD obtained a constraint on the cosmological constant, $\lambda > 0.6$, assuming the spatially flat universe. It plays a crucial role in this method that the angular diameter distance-redshift relation depends on the cosmological models through the cosmological parameters. First, using the angular diameter distance in the Friedmann-Lemaitre- Robertson-Walker universe, we show that one can hardly determine $\Omega$ by this method without the assumption of the spatially flat universe. We also investigate the effect of inhomogeneities of the universe by using the Dyer-Roeder angular diameter distance. It is shown that the effect of inhomogeneities can become too large to be ignored, particularly for a high density universe. As a result, this method cannot be taken as a clear cosmological test to determine $\Omega$ and $\lambda$, though it may provide a bound on $\Omega$ and $\lambda$. Moreover, we mention the uncertainty of the determination of the velocity dispersion, which is regarded as one of the most serious problems in this test.

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