{
  "id": "astro-ph/9611110",
  "version": "v1",
  "published": "1996-11-14T02:44:33.000Z",
  "updated": "1996-11-14T02:44:33.000Z",
  "title": "Critical Lines in Gravitational Lenses and the Determination of Cosmological Parameters",
  "authors": [
    "Hideki Asada"
  ],
  "comment": "16 pages, LaTeX(aaspp4), 11 postscript figures included; submitted to The Astrophysical Journal",
  "doi": "10.1086/304452",
  "categories": [
    "astro-ph"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1996-11-14T02:44:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cosmological parameters",
      "critical line",
      "gravitational lenses",
      "spatially flat universe",
      "determination"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 426006
    }
  }
}