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Astron. Astrophys. 344, 721-734 (1999)

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1. Introduction

The use of gravitational lensing statistics as a cosmological tool was first considered in detail by Turner et al. (1984); the influence of the cosmological constant was investigated thoroughly by Fukugita et al. (1992), building on the work of Turner (1990) and Fukugita et al. (1990). More recently, Kochanek (1996, hereafter K96, and references therein) and Falco et al. (1998) have laid the groundwork for using gravitational lensing statistics for the detailed analysis of extragalactic surveys. However, these analyses either have concentrated on a small subset of the possible cosmological models as described by the density parameter [FORMULA] and the cosmological constant [FORMULA], have used a simpler (singular) lens model or both. This analysis is the first time [FORMULA] and [FORMULA] have been used as independent parameters in conjunction with a non-singular lens model in an analysis of this type, complementing similar analyses with other emphases. (See Cheng & Krauss (1999) for a discussion of the importance of including a core radius.) Also, we include enough of the [FORMULA]-[FORMULA] plane to avoid neglecting any possibly viable models; this also makes the comparison with a variety of other cosmological tests easier. This is especially important in light of the fact that many analyses (e.g. Perlmutter et al. 1998; Riess et al. 1998; Schmidt et al. 1998; Carlberg et al. 1998a; Lineweaver 1998; Guerra et al. 1998; Daly et al. 1998) are now suggesting that our universe may contain a significant cosmological constant and be non-flat.

The plan of this paper is as follows. Sect. 2 reviews the groundwork and serves to define our notation. In Sect. 3 we specify the observational data and selection functions we use and formulate prior information about the parameters [FORMULA] and [FORMULA]. Sect. 4 describes the parametric submodels we use and the numerical computations we perform. In Sect. 5 we discuss our results and compare them with others. Sect. 6 presents our summary and conclusions.

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© European Southern Observatory (ESO) 1999

Online publication: March 29, 1999